Become a Calculus 2 Master by Udemy
Learn everything from Calculus 2, then test your knowledge with 830+ practice questions
Course Highlights
- Integrals, including approximating area, the dreaded Fundamental Theorem of Calculus, and every kind of integration technique
- Applications of Integrals, including volume of revolution with disks, washers and shells, and all kinds of real world applications
- Polar & Parametric, including how to sketch polar curves and find the area bounded by polar curves
- Sequences & Series, including all the convergence tests, and Taylor and Maclaurin series
Skills you will learn!
Curriculum
4 Topics
What we'll learn in this course
How to get the most out of this course
Download the formula sheet
The EVERYTHING download
17 Topics
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. :)
10 Topics
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. :)
15 Topics
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. :)
14 Topics
Introduction to other approximation methods
Over and underestimation
Over and underestimation
Limit process to find area on [ab]
Limit process to find area on [ab]
Limit process to find area on [-aa]
Limit process to find area on [-aa]
Trapezoidal rule
Trapezoidal rule
Trapezoidal rule
Simpson's rule
Simpson's rule
Simpson's rule
BONUS! Extra practice problems. :)
9 Topics
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. :)
10 Topics
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. :)
8 Topics
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. :)
16 Topics
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. :)
19 Topics
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. :)
23 Topics
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. :)
8 Topics
Introduction to hyperbolic integrals
Hyperbolic integrals
Hyperbolic integrals
Hyperbolic integrals
Inverse hyperbolic integrals
Inverse hyperbolic integrals
Inverse hyperbolic integrals
BONUS! Extra practice problems. :)
16 Topics
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. :)
19 Topics
Introduction to improper integrals
What makes an integral improper?
Improper integrals
Case 1 [ainfinity)
Case 1 [ainfinity)
Case 2 (-infinityb]
Case 2 (-infinityb]
Case 3 (-infinityinfinity)
Case 3 (-infinityinfinity)
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. :)
4 Topics
Introduction to reduction formulas
Integrals using reduction formulas
Integrals using reduction formulas
BONUS! Extra practice problems. :)
11 Topics
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. :)
8 Topics
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. :)
8 Topics
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. :)
8 Topics
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. :)
22 Topics
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. :)
14 Topics
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. :)
22 Topics
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. :)
7 Topics
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. :)
18 Topics
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. :)
5 Topics
Introduction to probability
Probability density
Probability density
Probability density
BONUS! Extra practice problems. :)
9 Topics
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. :)
14 Topics
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. :)
25 Topics
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. :)
18 Topics
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. :)
30 Topics
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. :)
23 Topics
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. :)
7 Topics
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. :)
13 Topics
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. :)
8 Topics
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. :)
14 Topics
Introduction to basic convergence tests
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. :)
11 Topics
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. :)
13 Topics
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. :)
8 Topics
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. :)
28 Topics
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. :)
11 Topics
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. :)
19 Topics
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. :)
4 Topics
Practice final exam #1 (optional)
Practice final exam #2 (optional)
Calculus 2 final exam
Wrap-up
Become a Calculus 2 Master
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