Welcome, we solved these typical calculus problems to help you see how calculus is "done". It is important to learn how to write mathematics and we hope these problems help you see some examples of good mathematical communication. We also hope you find the videos we prepared at:

are useful as you study calculus this semester.

- Basic Antiderivatives (should know from Math 131 or your previous Calculus course)
- Basic u-substitution problems (should know from Math 131 or your previous Calculus course)
- Integration involving combination of basic techniques (should know from Math 131 or your previous Calculus course)
- Integrals whose solution involves basic algebra or trigonometric insight (should know from Math 131 or your previous Calculus course)
- Sample integrals from Calculus I and Answers. (should know from Math 131 or your previous Calculus course)
- Test 1 from Math 131 and its solution
- Test 2 from Math 131 and its solution
- Test 3 from Math 131 and its solution
- Test 4 from Math 131 and its solution

Warning: there are a few errors in the documents below. Many of these are found as I work through these pdfs in the videos provided in:

Playlist for Math 132: Calculus II with analytic geometry

- Topic 1: Integration By Parts (IBP).
- Topic 2: Integration of trigonometric functions.
- Topic 3: Integration by the implicit substitution using trigonometric or hyperbolic functions.
- Topic 4: Integration of basic rational functions and the technique of partial fractions. That is, integration of rational functions via the partial fractal decomposition.
- Topic 5: Integration examples which involve multiple techniques.
- Topic 6: Numerical or Approximate Integration via Left, Right, Midpoint, Trapezoid or Simpson's Rules.
- Topic 7: Calculation of the area of a surface formed by revolving a curve.
- Topic 8: Calculation of arclength.
- Topic 9: Improper Integration; integrals which involve infinite bounds and/or divergent integrands.
- Topic 10: Applications of integration to physics; work done by a variable force.
- Topic 11: Application of Integration to probability. Normalization of density functions.
- Topic 12: Examples of Sequences and their limits.
- Topic 13: Examples of Series, definition of series in terms of sequence of partial sums.
- Topic 14: Geometric series examples.
- Topic 15: Integral Test and approximation of series with partial sum.
- Topic 16: The P-series.
- Topic 17: Direct and Limit Comparision Tests and Examples.
- Topic 18: Alternating Series and the Alternating Series Estimation Theorem.
- Topic 19: Absolute Convergence and the Ratio and Root Tests.
- Topic 20: Big Picture of How to Analyze Convergence or Divergence of a given series; examples and a flowchart.
- Topic 21: Power Series and the Interval of Convergence (IOC) and Radius of Convergence (ROC).
- Topic 22: Geometric Series Techniques; on term-by-term calculus for power series and how to use the geometric series in tandem to study power series.
- Topic 23: : Taylor Series and Binomial Series Calculation
- Topic 24: Taylor Polynomials, proof of Taylor's Theorem and applications.
- Topic 25: Test 3 of Math 132 from Fall 2009 and the solution to Test 3 of Math 132 from Fall 2009 concerning power series calculation.
- Topic 26: Test 4 of Math 132 from Spring 2011 and the solution to Test 4 of Math 132 from Spring 2011 concerning power series calculation.
- Topic 27: Test 3 of Math 132 from Fall 2016 and the solution to Test 3 of Math 132 from Fall 2016 (series and power series)
- Topic 28: Parametric Curves in the Plane.
- Topic 29: Calculus of Parametric Curves.
- Topic 30: Polar Coordinates.
- Topic 31: Calculus in Polar Coordinates.
- Topic 32: Problem Set II solution of Math 132 from Spring 2011. On parametrizations and polar coordinate.
- Topic 33: Quiz 2 of Math 132 from Spring 2011 and the solution to Quiz 2 of Math 132 from Spring 2011 (covers parametric curves and polar coordinates).
- Topic 34: Test 2 of Math 132 from Spring 2011 and the solution to Test 2 of Math 132 from Spring 2011 (covers parametric curves and polar coordinates).
- Topic 35: Terminology for Differential Equations.
- Topic 36: Direction Fields and Euler's Method.
- Topic 37: Separation of Variables and select applications involving first order DEqns.
- Topic 38: Integrating Factor Technique.
- Topic 39: Solved homework on differential equations.
- Topic 40: Quiz 5 of Math 132 from Fall 2016 and the solution to Quiz 5 of Math 132 from Fall 2016 on differential equations.
- Topic 41: Final Exam of Math 132 from Spring 2011 notice this is comprehensive.