Below is the course syllabus for MATH 101. Section numbers refer to the course textbook by Stewart.
Areas and distances (5.1), the definite integral (5.2), the Fundamental Theorem of Calculus (5.3), indefinite integrals and the Net Change Theorem (5.4), the Substitution Rule (5.5).
Applications of integration
Areas between curves (6.1), volumes (6.2), work (6.4), average value of a function (6.5). Note that we will omit volumes by cylindrical shells (6.3); please do not use this technique even if you know it.
Techniques of integration
Integration by parts (7.1, but ignore reduction formulas such as example 6), trigonometric integrals (7.2, but ignore sin mx and cos nx on page 476), trigonometric substitutions (7.3, but ignore hyperbolic functions like cosh x), integration of rational functions by partial fractions (7.4, but ignore case IV), approximate integration (7.7), improper integrals (7.8). Note that we will omit integration using tables and computer algebra systems (7.6). Strategy for integration (7.5) is a summary of the first four sections in this chapter; we will not cover it explicitly, but it is an excellent review for sections 7.1–7.4.
Further applications of integration
We will learn about the centre of mass from section 8.3. You may ignore the rest of that section, including hydrostatic pressure and force and the theorem of Pappus, and the rest of chapter 8 as well.
We will learn about separable differential equations from section 9.3. You may ignore the rest of that section, including orthogonal trajectories and direction fields, and the rest of chapter 9 as well.
Infinite sequences and series
Sequences (11.1, but ignore Definitions 2 and 5), series (11.2), the Integral Test (11.3, but ignore estimates of sums), the Comparison Tests (11.4, but ignore estimating sums), alternating series (11.5), absolute convergence and the ratio test (11.6, but ignore the root test), power series (11.8), representations of functions as power series (11.9), Taylor and Maclaurin series (11.10, but ignore the binomial series, multiplication and division of power series, and the remainder term for Taylor series). Strategy for testing series (11.7) is a summary of the first six sections in this chapter; we will not cover it explicitly, but it is an excellent review for sections 11.1–11.6.
The list of MATH 101 learning outcomes from last year is very helpful—it contains specific items of knowledge and specific skills that you will be gaining in connection with the topics above.