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    Become a Calculus 2 Master

    BY
    Udemy

    Gain a hands-on understanding of the core principles and strategies associated with Calculus to become a master in mathematics.

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    Mode

    Online

    Fees

    ₹ 449 3099

    Quick Facts

    particular details
    Medium of instructions English
    Mode of learning Self study
    Mode of Delivery Video and Text Based

    Course overview

    Become a Calculus 2 Master certification course was established by Krista King, a Certified Math Teacher, and is accessible on Udemy which is designed for students who wish to learn the fundamental and advanced concepts and principles of calculus. Become a Calculus 2 Master online course by Udemy focuses on providing students with a practical understanding of the tools and techniques used in calculus to solve various equations.

    Become a Calculus 2 Master online classes contain almost 30.5 hours of lectures, 194 articles, and 375 downloadable study resources on integrals, including estimating area, the dreaded fundamental theorem of calculus, and every type of integration technique. Students will learn how to use integration, integrals, sequence, series, polar, and parametric in a variety of subjects, including physics, biology, economics, geometry, probability, and more.

    The highlights

    • Certificate of completion
    • Self-paced course
    • 30.5 hours of pre-recorded video content
    • 194 articles
    • 375 downloadable resources
    • Quizzes

    Program offerings

    • Online course
    • Learning resources. 30-day money-back guarantee
    • Unlimited access
    • Accessible on mobile devices and tv

    Course and certificate fees

    Fees information
    ₹ 449  ₹3,099
    certificate availability

    Yes

    certificate providing authority

    Udemy

    Who it is for

    Teacher Scientist

    What you will learn

    Mathematical skill

    After completing the Become a Calculus 2 Master online certification, students will acquire a deeper knowledge of the fundamentals of mathematics and will develop an understanding of the concepts associated with calculus. Students will study foundational theory, integration, integrals, polar curves, parametric curves, sequences, series, and convergence, among other things. Students will also learn the use of calculus in subjects such as physics, economics, biology, probability, and geometry as well as operations such as partial fractions, trigonometric integrals, average value, arc length, and the area between curves.

    The syllabus

    Getting started

    • Hi! START HERE: Course overview
    • Download the Calc 2 formula sheet
    • The EVERYTHING download

    Integrals - Antiderivatives and indefinite integrals

    • Introduction to antiderivatives and indefinite integrals
    • Antiderivatives and indefinite integrals
    • Indefinite integrals
    • Indefinite integrals
    • Indefinite integrals
    • Properties of integrals
    • Properties of integrals
    • Find f given f''
    • Find f given f''
    • Find f given f'''
    • Find f given f'''
    • Initial value problems
    • Initial value problems
    • Initial value problems
    • Find f given f'' and initial conditions
    • Find f given f'' and initial conditions
    • BONUS! Extra practice problems. :)

    Integrals - Definite integrals

    • Introduction to definite integrals
    • Definite integrals
    • Definite integrals
    • Definite integrals
    • Area under or enclosed by the graph
    • Area under or enclosed by the graph
    • Definite integrals of even and odd functions
    • Definite integrals of even and odd functions
    • Definite integrals of even and odd functions
    • BONUS! Extra practice problems. :)

    Integrals - Riemann sums

    • Introduction to riemann sums
    • Summation notation, finding the sum
    • Summation notation, finding the sum
    • Summation notation, expanding
    • Summation notation, expanding
    • Summation notation, collapsing
    • Summation notation, collapsing
    • Riemann sums
    • Riemann sums, left endpoints
    • Riemann sums, left endpoints
    • Riemann sums, right endpoints
    • Riemann sums, right endpoints
    • Riemann sums, midpoints
    • Riemann sums, midpoints
    • BONUS! Extra practice problems. :)

    Integrals - Other approximation methods

    • Introduction to other approximation methods
    • Over and underestimation
    • Over and underestimation
    • Limit process to find area on [a,b]
    • Limit process to find area on [a,b]
    • Limit process to find area on [-a,a]
    • Limit process to find area on [-a,a]
    • Trapezoidal rule
    • Trapezoidal rule
    • Trapezoidal rule
    • Simpson's rule
    • Simpson's rule
    • Simpson's rule
    • BONUS! Extra practice problems. :)

    Integrals - Error bounds

    • Introduction to error bounds
    • Error bounds
    • Midpoint rule error bound
    • Midpoint rule error bound
    • Trapezoidal rule error bound
    • Trapezoidal rule error bound
    • Simpson's rule error bound
    • Simpson's rule error bound
    • BONUS! Extra practice problems. :)

    Integrals - Fundamental theorem of calculus

    • Introduction to fundamental theorem of calculus
    • Part 1
    • Part 1
    • Part 1
    • Part 2
    • Part 2
    • Part 2
    • Net change theorem
    • Net change theorem
    • BONUS! Extra practice problems. :)

    Integrals - U-substitution

    • Introduction to u-substitution
    • U-substitution
    • U-substitution
    • U-substitution
    • U-substitution in definite integrals
    • U-substitution in definite integrals
    • U-substitution in definite integrals
    • BONUS! Extra practice problems. :)

    Integrals - Integration by parts

    • Introduction to integration by parts
    • Integration by parts
    • Integration by parts
    • Integration by parts
    • Integration by parts two times
    • Integration by parts two times
    • Integration by parts two times
    • Integration by parts three times
    • Integration by parts three times
    • Integration by parts with u-substitution
    • Integration by parts with u-substitution
    • Prove the reduction formula
    • Tabular integration
    • Tabular integration
    • Tabular integration
    • BONUS! Extra practice problems. :)

    Integrals - Partial fractions

    • Introduction to partial fractions
    • Partial fractions
    • Distinct linear factors
    • Distinct linear factors, example 2
    • Distinct linear factors, example 3
    • Distinct linear factors
    • Distinct quadratic factors
    • Distinct quadratic factors, example 2
    • Distinct quadratic factors, example 3
    • Distinct quadratic factors
    • Repeated linear factors
    • Repeated linear factors
    • Repeated quadratic factors
    • Repeated quadratic factors, example 2
    • Repeated quadratic factors
    • Rationalizing substitutions
    • Rationalizing substitutions
    • Rationalizing substitutions
    • BONUS! Extra practice problems. :)

    Integrals - Trigonometric integrals

    • Introduction to trigonometric integrals
    • Trigonometric integrals
    • Trigonometric integrals
    • Trigonometric integrals, example 2
    • Trigonometric integrals
    • sin^m cos^n, odd m
    • sin^m cos^n, odd m
    • sin^m cos^n, odd n
    • sin^m cos^n, odd n
    • sin^m cos^n, m and n even
    • sin^m cos^n, m and n even
    • tan^m sec^n, odd m
    • tan^m sec^n, odd m
    • tan^m sec^n, even n
    • tan^m sec^n, even n, example 2
    • tan^m sec^n, even n
    • sin(mx) cos(nx)
    • sin(mx) cos(nx)
    • sin(mx) sin(nx)
    • sin(mx) sin(nx)
    • cos(mx) cos(nx)
    • cos(mx) cos(nx)
    • BONUS! Extra practice problems. :)

    Integrals - Hyperbolic integrals

    • Introduction to hyperbolic integrals
    • Hyperbolic integrals
    • Hyperbolic integrals
    • Hyperbolic integrals
    • Inverse hyperbolic integrals
    • Inverse hyperbolic integrals
    • Inverse hyperbolic integrals
    • BONUS! Extra practice problems. :)

    Integrals - Trigonometric substitution

    • Introduction to trigonometric substitution
    • Trigonometric substitution
    • Trigonometric substitution setup
    • Trigonometric substitution setup
    • Trigonometric substitution with secant
    • Trigonometric substitution with secant
    • Trigonometric substitution with sine
    • Trigonometric substitution with sine, example 2
    • Trigonometric substitution with sine
    • Trigonometric substitution with tangent
    • Trigonometric substitution with tangent, example 2
    • Trigonometric substitution with tangent
    • Quadratic functions
    • Quadratic functions
    • Quadratic functions
    • BONUS! Extra practice problems. :)

    Integrals - Improper integrals

    • Introduction to improper integrals
    • What makes an integral improper?
    • Improper integrals
    • Case 1 [a,infinity)
    • Case 1 [a,infinity)
    • Case 2 (-infinity,b]
    • Case 2 (-infinity,b]
    • Case 3 (-infinity,infinity)
    • Case 3 (-infinity,infinity)
    • Case 4 (discontinuity at b)
    • Case 4 (discontinuity at b)
    • Case 5 (discontinuity at a)
    • Case 5 (discontinuity at a)
    • Case 6 (discontinuity between a and b)
    • Case 6 (discontinuity between a and b)
    • Comparison theorem
    • Comparison theorem
    • Comparison theorem
    • BONUS! Extra practice problems. :)

    Integrals - Reduction formulas

    • Introduction to reduction formulas
    • Integrals using reduction formulas
    • Integrals using reduction formulas
    • BONUS! Extra practice problems. :)

    Applications of Integrals - Area between curves

    • Introduction to area between curves
    • Area between curves
    • Upper and lower curves
    • Upper and lower curves
    • Left and right curves
    • Left and right curves
    • Sketching the area between curves
    • Sketching the area between curves
    • Dividing the area between curves into equal parts
    • Dividing the area between curves into equal parts
    • BONUS! Extra practice problems. :)

    Applications of Integrals - Arc length

    • Introduction to arc length
    • Arc length
    • Arc length of a curve in the form y=f(x)
    • Arc length of a curve in the form y=f(x)
    • Arc length of a curve in the form x=g(y)
    • Arc length of a curve in the form x=g(y)
    • Arc length using simpson's rule
    • BONUS! Extra practice problems. :)

    Applications of Integrals - Average value

    • Introduction to average value
    • Average value
    • Average value
    • Average value
    • Mean value theorem for integrals
    • Mean value theorem for integrals
    • Mean value theorem for integrals
    • BONUS! Extra practice problems. :)

    Applications of Integrals - Surface area of revolution

    • Introduction to surface area of revolution
    • Surface area of revolution
    • Surface area of revolution
    • Surface area of revolution using simpson's ule
    • Surface area of revolution
    • Surface of revolution equation
    • Surface of revolution equation
    • BONUS! Extra practice problems. :)

    Applications of Integrals - Volume of revolution

    • Introduction to volume of revolution
    • Disks
    • Disks, horizontal axis
    • Disks, horizontal axis
    • Disks, vertical axis
    • Disks, vertical axis, example 2
    • Disks, vertical axis
    • Disks, volume of the frustum
    • Disks, volume of the frustum
    • Washers
    • Washers, horizontal axis
    • Washers, horizontal axis, example 2
    • Washers, horizontal axis
    • Washers, vertical axis
    • Washers, vertical axis
    • Cylindrical shells
    • Cylindrical shells, horizontal axis
    • Cylindrical shells, horizontal axis
    • Cylindrical shells, vertical axis
    • Cylindrical shells, vertical axis, example 2
    • Cylindrical shells, vertical axis
    • BONUS! Extra practice problems. :)

    Applications of Integrals - Work

    • Introduction to work
    • Work done to lift a mass or weight
    • Work done to lift a mass or weight
    • Work done to lift a mass or weight
    • Work done on elastic springs
    • Work done on elastic springs
    • Work done on elastic springs
    • Work done to empty a tank
    • Work done to empty a tank
    • Work done to empty a tank
    • Work done by a variable force
    • Work done by a variable force
    • Work done by a variable force
    • BONUS! Extra practice problems. :)

    Applications of Integrals - Physics

    • Introduction to physics
    • Moments and center of mass of the system
    • Moments of the system
    • Moments of the system
    • Moments of the system, x-axis
    • Moments of the system, x-axis
    • Center of mass of the system
    • Center of mass of the system
    • Center of mass of the system, x-axis
    • Center of mass of the system, x-axis
    • Hydrostatic pressure and force
    • Hydrostatic pressure
    • Hydrostatic pressure
    • Hydrostatic force
    • Hydrostatic force
    • Vertical motion
    • Vertical motion
    • Vertical motion
    • Rectilinear motion
    • Rectilinear motion
    • Rectilinear motion
    • BONUS! Extra practice problems. :)

    Applications of Integrals - Geometry

    • Introduction to geometry
    • Centroids of plane regions
    • Centroids of plane regions
    • Centroids of plane regions
    • Area of the triangle with the given vertices
    • Area of the triangle with the given vertices
    • BONUS! Extra practice problems. :)

    Applications of Integrals - Economics

    • Introduction to economics
    • Present and future value
    • Single deposit, compounded n times, future value
    • Single deposit, compounded n times, future value
    • Single deposit, compounded n times, present value
    • Single deposit, compounded n times, present value
    • Single deposit, compounded continuously, future value
    • Single deposit, compounded continuously, future value
    • Single deposit, compounded continuously, present value
    • Single deposit, compounded continuously, present value
    • Income stream, compounded continuously, future value
    • Income stream, compounded continuously, future value
    • Income stream, compounded continuously, present value
    • Income stream, compounded continuously, present value
    • Consumer and producer surplus
    • Consumer and producer surplus
    • Consumer and producer surplus
    • BONUS! Extra practice problems. :)

    Applications of Integrals - Probability

    • Introduction to probability
    • Probability density
    • Probability density
    • Probability density
    • BONUS! Extra practice problems. :)

    Applications of Integrals - Biology

    • Introduction to biology
    • Cardiac output
    • Cardiac output
    • Poiseuille's law
    • Poiseuille's law
    • Theorem of pappus
    • Theorem of pappus
    • Theorem of pappus
    • BONUS! Extra practice problems. :)

    Polar & Parametric - Parametric curves

    • Introduction to parametric curves
    • Eliminating the parameter
    • Eliminating the parameter
    • Eliminating the parameter
    • Derivative of a parametric curve
    • Derivative of a parametric curve
    • Derivative of a parametric curve
    • Second derivative of a parametric curve
    • Second derivative of a parametric curve
    • Second derivative of a parametric curve
    • Sketching parametric curves by plotting points
    • Sketching parametric curves by plotting points
    • Sketching parametric curves by plotting points
    • BONUS! Extra practice problems. :)

    Polar & Parametric - Calculus with parametric curves

    • Introduction to calculus with parametric curves
    • Tangent line to the parametric curve
    • Tangent line to the parametric curve
    • Tangent line to the parametric curve
    • Area under a parametric curve
    • Area under a parametric curve
    • Area under a parametric curve
    • Area under one arc or loop of a parametric curve
    • Area under one arc or loop of a parametric curve
    • Area under one arc or loop of a parametric curve
    • Arc length of a parametric curve
    • Arc length of a parametric curve
    • Arc length, particle motion
    • Arc length, simpson's rule
    • Arc length of a parametric curve
    • Surface area of revolution of a parametric curve, horizontal axis
    • Surface area of revolution of a parametric curve, horizontal axis
    • Surface area of revolution of a parametric curve, horizontal axis
    • Surface area of revolution of a parametric curve, vertical axis
    • Surface area of revolution of a parametric curve, vertical axis
    • Surface area of revolution of a parametric curve, vertical axis
    • Volume of revolution with parametric curves
    • Volume of revolution with parametric curves
    • Volume of revolution with parametric curves
    • BONUS! Extra practice problems. :)

    Polar & Parametric - Polar curves

    • Introduction to polar curves
    • Converting to polar coordinates
    • Converting to polar coordinates
    • Converting to polar coordinates
    • Converting rectangular equations
    • Converting rectangular equations
    • Converting rectangular equations
    • Converting polar equations
    • Converting polar equations
    • Converting polar equations
    • Distance between polar points
    • Distance between polar points
    • Distance between polar points
    • Sketching polar curves
    • Sketching polar curves
    • Sketching polar curves from cartesian curves
    • Sketching polar curves
    • BONUS! Extra practice problems. :)

    Polar & Parametric - Calculus with polar curves

    • Introduction to calculus with polar curves
    • Tangent line to the polar curve
    • Tangent line to the polar curve
    • Tangent line to the polar curve
    • Vertical and horizontal tangent lines to the polar curve
    • Vertical and horizontal tangent lines to the polar curve
    • Vertical and horizontal tangent lines to the polar curve
    • Intersection of polar curves
    • Intersection of polar curves
    • Intersection of polar curves
    • Area inside a polar curve
    • Area inside a polar curve
    • Area inside a polar curve
    • Area bounded by one loop of a polar curve
    • Area bounded by one loop of a polar curve
    • Area bounded by one loop of a polar curve
    • Area between polar curves
    • Area between polar curves
    • Area between polar curves
    • Area inside both polar curves
    • Area inside both polar curves
    • Area inside both polar curves
    • Arc length of a polar curve
    • Arc length of a polar curve
    • Arc length of a polar curve, example 2
    • Arc length of a polar curve
    • Surface area of revolution of a polar curve
    • Surface area of revolution of a polar curve
    • Surface area of revolution of a polar curve
    • BONUS! Extra practice problems. :)

    Sequences & Series - Sequences

    • Introduction to sequences
    • Sequences vs. series
    • Sequences vs. series
    • Listing the first terms
    • Listing the first terms
    • Calculating the first terms
    • Calculating the first terms
    • Formula for the general term
    • Formula for the general term
    • Formula for the general term
    • Convergence of a sequence
    • Convergence of a sequence
    • Convergence of a sequence
    • Limit of a convergent sequence
    • Limit of a convergent sequence
    • Limit of a convergent sequence
    • Increasing, decreasing, and not monotonic
    • Increasing, decreasing, and not monotonic
    • Increasing, decreasing, and not monotonic
    • Bounded sequences
    • Bounded sequences
    • Bounded sequences
    • BONUS! Extra practice problems. :)

    Sequences & Series - Partial sums

    • Introduction to partial sums
    • Calculating the first terms of a sequence of partial sums
    • Calculating the first terms of a sequence of partial sums
    • Sum of the sequence of partial sums
    • Sum of the sequence of partial sums
    • Sum of the sequence of partial sums
    • BONUS! Extra practice problems. :)

    Sequences & Series - Geometric series

    • Introduction to geometric series
    • Geometric series test
    • Geometric series test
    • Geometric series test
    • Sum of the geometric series
    • Sum of the geometric series
    • Sum of the geometric series
    • Values for which the series converges
    • Values for which the series converges
    • Geometric series for repeating decimals
    • Geometric series for repeating decimals
    • Geometric series for repeating decimals
    • BONUS! Extra practice problems. :)

    Sequences & Series - Telescoping series

    • Introduction to telescoping series
    • Convergence of a telescoping series
    • Convergence of a telescoping series
    • Convergence of a telescoping series
    • Sum of a telescoping series
    • Sum of a telescoping series
    • Sum of a telescoping series
    • BONUS! Extra practice problems. :)

    Sequences & Series - Basic convergence tests

    • Introduction to basic convergence tests
    • Recognizing types of series
    • Strategy for testing series
    • Limit vs. sum of the series
    • Limit vs. sum of the series
    • Limit vs. sum of the series
    • Integral test
    • Integral test
    • Integral test
    • p-series test
    • p-series test
    • p-series
    • nth term test
    • nth term test
    • nth term test
    • BONUS! Extra practice problems. :)

    Sequences & Series - Comparison tests

    • Introduction to comparison tests
    • Comparison test
    • Comparison test
    • Comparison test
    • Limit comparison test
    • Limit comparison test
    • Limit comparison test
    • Error or remainder of a series
    • Error or remainder of a series
    • Error or remainder of a series
    • BONUS! Extra practice problems. :)

    Sequences & Series - Ratio and root tests

    • Introduction to ratio and root tests
    • Ratio test
    • Ratio test
    • Ratio test
    • Ratio test with factorials
    • Ratio test with factorials
    • Root test
    • Root test
    • Root test
    • Absolute and conditional convergence
    • Absolute and conditional convergence
    • Absolute and conditional convergence
    • BONUS! Extra practice problems. :)

    Sequences & Series - Alternating series test

    • Introduction to alternating series test
    • Alternating series test
    • Alternating series test
    • Alternating series test
    • Alternating series estimation theorem
    • Alternating series estimation theorem
    • Alternating series estimation theorem
    • BONUS! Extra practice problems. :)

    Sequences & Series - Power series

    • Introduction to power series
    • Power series representation
    • Power series representation
    • Power series representation
    • Power series multiplication
    • Power series multiplication
    • Power series multiplication
    • Power series division
    • Power series division
    • Power series division
    • Power series differentiation
    • Power series differentiation
    • Power series differentiation
    • Radius and interval of convergence
    • Radius of convergence
    • Radius of convergence
    • Interval of convergence
    • Interval of convergence
    • Estimating definite integrals
    • Estimating definite integrals
    • Estimating definite integrals
    • Estimating indefinite integrals
    • Estimating indefinite integrals
    • Estimating indefinite integrals
    • Binomial series
    • Binomial series
    • Binomial series
    • BONUS! Extra practice problems. :)

    Sequences & Series - Taylor series

    • Introduction to Taylor series
    • Taylor series
    • Taylor series
    • Taylor series
    • Radius and interval of convergence of a Taylor series
    • Radius and interval of convergence of a Taylor series
    • Radius and interval of convergence of a Taylor series
    • Taylor's inequality
    • Taylor's inequality
    • Taylor's inequality
    • BONUS! Extra practice problems. :)

    Sequences & Series - Maclaurin series

    • Introduction to Maclaurin series
    • Maclaurin series
    • Maclaurin series
    • Maclaurin series
    • Sum of the Maclaurin series
    • Sum of the Maclaurin series
    • Sum of the Maclaurin series
    • Radius and interval of convergence of a Maclaurin series
    • Radius and interval of convergence of a Maclaurin series
    • Radius and interval of convergence of a Maclaurin series
    • Indefinite integral as an infinite series
    • Indefinite integral as an infinite series
    • Maclaurin series to estimate an indefinite integral
    • Maclaurin series to estimate an indefinite integral
    • Maclaurin series to estimate a definite integral
    • Maclaurin series to estimate a definite integral
    • Maclaurin series to evaluate a limit
    • Maclaurin series to evaluate a limit
    • BONUS! Extra practice problems. :)

    Final exam and wrap-up

    • Practice final exam #1 (optional)
    • Practice final exam #2 (optional)
    • Calculus 2 final exam
    • Wrap-up

    Instructors

    Ms Krista King
    Instructor
    Udemy

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