Science:Math Exam Resources/Courses/MATH101

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General Course Info

Visit the course main page here.

Midterm 1: Tuesday, Feb 25th 2014
Day of final exam: Friday, April 25th, 2014, 3:30PM

Available Practice Exams

Dynamic Course Syllabus

The full course syllabus can be found here.

Week 1. Areas and Distances (5.1) and the Definite Integral (5.2).

Learn about Riemann sums

Week 2. The Fundamental Theorem of Calculus (5.3). Indefinite integrals and the Net Change Theorem (5.4). The Substitution Rule (5.5).

Learn about The fundamental theorem of calculus

Learn about antiderivative sketching

Learn about net change theorem

Learn about substitution

Week 3. Areas between curves (6.1). Volumes (6.2).

Learn about calculating the area between curves

Learn about volumes from cross-section

Week 4. Work (6.4). Average Value of a Function (6.5). Integration by Parts (7.1 but ignore reduction formulas).

Learn about work

Learn about average value of a function

Learn about integration by parts

Week 5. Trigonometric Integrals (7.2 but ignore sin mx, cos nx, etc.). Trigonometric substitutions (7.3 but ignore inverse secant and inverse hyperbolic substitutions). Integration of rational functions by partial fractions (7.4 but ignore CASE VI: Q(x) contains a repeated irreducible quadratic factor).

Practice integrals uncategorized, involving any technique

Learn about trigonometric integrals

Learn about trigonometric substitution

Learn about partial fractions

Week 6. Strategy for integration (7.5). Approximate integration (7.7). Improper integrals (7.8).

Learn about approximate integration: trapezoidal rule

Learn about approximate integration: Simpson's rule

Learn about improper integrals

Week 7. Applications to Physics and Engineering (8.3 but ignore hydrostatic pressure and force and the Theorem of Pappus). Separable equations (9.3 but ignore orthogonal trajectories).

Learn about applications of physics: center of mass

Learn about applications of physics: centroid

Learn about applications of physics: Hooke's law

Learn about separation of variables

Week 8. Sequences (11.1 but ignore definitions 2 and 5, Example 6, and the proof of the Monotonic Sequence Theorem). Series (11.2).

Learn about sequences

Learn about series

Week 9. The integral test (11.3 but ignore estimating the sum of a series and the proof of the integral test). Comparison tests (11.4 but ignore estimating sums).

Learn about integral comparison test

Week 10. Alternating series (11.5). Absolute convergence and the ratio test (11.6 but ignore the root test).

Learn about alternating series

Learn about series (and tests for convergence)

Week 11. Power series (11.8). Representations of functions as power series (11.9).

Learn about power series

Week 12. Taylor and Maclaurin series (11.10 but ignore binomial series)

Learn about Taylor series

Learn about Taylor's remainder theorem

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