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2","description":"

🌟🌟🌟🌟🌟 \"Thank you Krista once again! I love calculus so much. I had to drop out of high school due to some reasons, then I tried to learn calculus as much as I could from books, but I found it difficult. But, now I am so happy that I can learn my favorite subject with an easy explanation with every detail.\"\n

🌟🌟🌟🌟🌟 \"Krista does an excellent job of explaining the smallest details in every example. She never assumes you understood where a number came from. I've learned much more from her than I have my own lecture videos at ASU!\"\n

The curriculum includes:\n

Antiderivatives and indefinite integrals\n\t
1. Indefinite integrals
2. Properties of integrals
3. Find f given f''
4. Find f given f'''
5. Initial value problems
Definite integrals\n\t
1. Definite integrals
2. Area under or enclosed by the graph
3. Definite integrals of even functions and odd functions
Riemann sums\n\t
1. Summation notation, finding the sum, expanding, collapsing
2. Riemann sums with left endpoints, right endpoints, and midpoints
3. Overestimation and underestimation
4. Limit process to find area on [a,b] and [-a,a]
5. Trapezoidal rule
6. Simpson's rule
Error bounds\n\t
1. Midpoint rule error bound
2. Trapezoidal rule error bound
3. Simpson's rule error bound
Fundamental theorem of calculus (FTC)\n\t
1. Part 1 of the FTC
2. Part 2 of the FTC
3. Net change theorem
U-substitution\n\t
1. U-substitution
2. U-substitution in definite integrals
Integration by parts\n\t
1. Integration by parts
2. Integration by parts two times and three times
3. Integration by parts with u-substitution
4. Prove the reduction formula
5. Tabular integration
Partial fractions\n\t
1. Distinct linear factors
2. Distinct quadratic factors
3. Repeated linear factors
4. Repeated quadratic factors
5. Rationalizing substitutions
6. How to factor a difficult denominator
7. Two ways to find the constants
Trigonometric integrals\n\t
1. Trigonometric integrals
2. sin^m cos^n, odd m
3. sin^m cos^n, odd n
4. sin^m cos^n, m and n even
5. tan^m sec^n, odd m
6. tan^m sec^n, even n
7. sin(mx) cos(nx)
8. sin(mx) cos(nx)
9. cos(mx) cos(nx)
Hyperbolic integrals\n\t
1. Hyperbolic integrals
2. Inverse hyperbolic integrals
Trigonometric substitution\n\t
1. Setting up for trig substitution problems
2. Secant substitutions
3. Sine substitutions
4. Tangent substitutions
5. Quadratic functions
Improper integrals\n\t
1. Improper integrals
2. Case 1 [a,infinity)
3. Case 2 (-infinity,b]
4. Case 3 (-infinity,infinity)
5. Case 4 (discontinuity at b)
6. Case 5 (discontinuity at a)
7. Case 6 (discontinuity between a and b)
8. Comparison theorem
Reduction formulas
Area between curves\n\t
1. Area between curves
2. Area between upper and lower curves
3. Area between left and right curves
4. Sketching area between curves
5. Dividing the area between curves into equal parts
Arc length\n\t
1. Arc length of a curve y=f(x)
2. Arc length of a curve x=g(y)
3. Arc length using Simpson's rule
Average value\n\t
1. Average value
2. Mean value theorem for integrals
Surface area of revolution\n\t
1. Surface area of revolution
2. Surface area of revolution using Simpson's rule
3. Surface of revolution equation
Volume of revolution\n\t
1. Disks with vertical and horizontal axes of revolution
2. Disks, volume of the frustum
3. Washers with vertical and horizontal axes of revolution
4. Cylindrical shells with vertical and horizontal axes of revolution
Work\n\t
1. Work done to lift a mass or weight
2. Work done on elastic springs
3. Work done to empty a tank
4. Work done by a variable force
Physics\n\t
1. Moments of the system
2. Center of mass of the system
3. Hydrostatic pressure and hydrostatic force
4. Vertical motion
5. Rectilinear motion
Geometry\n\t
1. Centroids of plane regions
2. Centroids of plane regions using Simpson's rule
3. Area of the triangle with the given vertices
Economics\n\t
1. Present value and future value
2. Single deposit, compounded n times
3. Single deposit, compounded continuously
4. Income stream, compounded continuously
5. Consumer surplus and producer surplus
Probability\n\t
1. Probability density
Biology\n\t
1. Cardiac output
2. Cardiac output using Simpson's rule
3. Poiseuille's law
4. Theorem of Pappus
Introduction to parametric curves\n\t
1. Eliminating the parameter
2. Derivatives of parametric curves
3. Second derivatives of parametric curves
4. Sketching parametric curves by plotting points
Calculus with parametric curves\n\t
1. Tangent lines of parametric curves
2. Area under a parametric curve
3. Area under one arc or loop of a parametric curve
4. Arc length of a parametric curves
5. Surface area of revolution of a parametric curves, horizontal axis and vertical axis
6. Volume of revolution of a parametric curves
Introduction to polar curves\n\t
1. Polar coordinates
2. Converting rectangular equations
3. Converting polar equations
4. Distance between points
5. Sketching polar curves
Calculus with polar curves\n\t
1. Tangent line to the polar curve
2. Vertical and horizontal tangent lines to a polar curve
3. Intersection of polar curves
4. Area inside a polar curve
5. Area bounded by one loop of a polar curve
6. Area between polar curves
7. Area inside both polar curves
8. Arc length of a polar curve
9. Surface area of revolution of a polar curve
Introduction to sequences\n\t
1. Sequences vs. series
2. Listing the first terms
3. Calculating the first terms
4. Formula for the general term
5. Convergence of a sequence
6. Limit of a convergent sequence
7. Increasing, decreasing, and not monotonic
8. Bounded sequences
Partial sums\n\t
1. Calculating the first terms of a series of partial sums
2. Sum of the series of partial sums
Geometric series\n\t
1. Geometric series test
2. Sum of the series
3. Values for which the series converges
4. Repeating decimals
Telescoping series\n\t
1. Convergence
2. Sum of the series
Basic convergence tests
\n\t
1. Recognizing types of series
2. Limit vs. sum of the series
3. Integral test
4. p-series test
5. nth term test (aka divergence test, zero test)
Comparison tests\n\t
1. Comparison test
2. Limit comparison test
3. Error of a series (remainder of a series)
Ratio and root tests\n\t
1. Ratio test
2. Ratio test with factorials
3. Root test
4. Absolute and conditional convergence
Alternating series test\n\t
1. Alternating series test
2. Alternating series estimation theorem
Power series\n\t
1. Power series representation
2. Power series multiplication and division
3. Power series differentiation
4. Radius of convergence, interval of convergence
5. Estimating definite integrals, estimating indefinite integrals
6. Binomial series
Taylor series\n\t
1. Taylor series
2. Radius of a Taylor series, interval of convergence of a Taylor series
3. Taylor's inequality
Maclaurin series\n\t
1. Maclaurin series
2. Sum of a Maclaurin series
3. Radius of a Maclaurin series, interval of convergence of a Maclaurin series
4. Evaluating indefinite integrals as an infinite series
5. Estimating indefinite integrals
6. Estimating definite integrals
7. Evaluating limits

About the Author
\n

Krista King is a math tutor, online educator, and the creator of KristaKingMath.com. Her YouTube channel has more than 43.5 million views, and her online courses have helped more than 244,000 students.\n

\"Krista is very very quick to respond. I've had a few questions and I usually didn't have to wait much longer than a day to get an answer. Not only that, but she obviously spent time answering to make sure I understood the content.\" - Morgan Gray\n

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By signing up for the Calculus 2 course, you'll gain access to:\n

Calculus 2, and every other Krista King Math course
Step-by-step videos
Course notes and flashcards
Practice quizzes
Bonus practice workbooks
Comprehensive formula sheets
Summary study sheets
Practice final exams

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