To prepare: study assignments 30-40, all quizzes we have done this term, and the assignments/quizzes needed for the energy project (all of these are under the PRACTICE, HOMEWORK, SOLUTIONS, ETC. link. Study tour class notes, especially examples that we discussed. Read below for details. For extra practice, work on some of suggested problems for each section covered on the test. Any non-graphing calculator is allowed on all tests and quizzes. [However, for the final exam you will need Casio fx991 calculator; this means any of fx991MS, fx991MS+, fx991ES+, fx991ES+, fx991W, etc. which has two lines of display and no graphing.] Section 4.9: know what an antiderivative is, since you need it for computing definite integrals; all antiderivative formulas you need to memorize are in the table on page 345 (repeated on page 398). Sections 5.1, 5.2: you need to know how to calculate R_n, L_n, M_n for a small value of n (such as example 1 on page 360, or example 3(b) on page 366) and how to set up (but not calculate) formulas in general (such as the first line of the formula for R_n in example 2, page 362, or example 3(a) on page 366). Know definition of definite integral (from your notes, or box on page 372), and interpretation of definite integral as area or difference of areas (such as example 4 on page 377). Know properties of definite integrals (boxed formulas on pages 379-381) and study example 8 on page 381. Sections 5.3, 5.4: know statements of FTC1 (page 388) and FTC 2 (page 391); know how to use both parts, such as in examples 2, 4, 6-8 in section 5.3 or examples 4, 5 in Section 5.4. Sections 5.5, 7.1: review basic substitution and integration by parts in the context of evaluating definite integrals. Section 7.8: know definition of improper integrals. Study examples 1, 2, 3, 4; memorize formula (2) on page 523; study examples 5-8. Sections 6.1, 6.2: practice setting up area and volume formulas, both by integrating along the x-axis and along the y-axis. Typical cases: examples 2, 5, 6 in section 6.1 and examples 2-6 in Section 6.2. Section 9.1: know how to analyze DEs qualitatively, such as logistic equation (2) on page 581, or exercise #9. Section 9.2: know what a direction field is, and how it helps solve a differential equation graphically; study Example 1. Skip Euler's method. Section 9.3: technical section, practice separable equations and simplifying to obtain an explicit form for the solution. Section 9.4: memorize formula (2) on page 606; no need to memorize the solution of a logistic DEor Gompertz (will be given if needed) ; study example 2 on pages 609/610. Section 9.6: study example 1; study relevant questions from assignments and quizzes |