# Course Outline:

 Section(s) 1. Riemann Sums a. Examples 7.4, 7.5 b. Sigma Notation 7.4 c. Useful sums 7.4 d. Limits of sums 7.5 2. The Definite Integral a. Definition and notation 7.6, 7.5 b. Interpretations 7.5 (sort of) c. Sums, products and inequalities 7.6 d. Integrability 7.6 3. Antiderivatives a. Definition and notation 7.2 b. Uniqueness 7.2 c. The Fundamental Theorem of Calculus 7.6 d. The indefinite integral 7.2 4. Integration Rules a. Powers, sums 7.2 b. Trigonometric rules 7.3 c. Integration by substitution 7.3, 7.8 5. Applications of Integration a. Linear motion 7.7 b. Area under a curve, signed area 7.5, 8.1 c. Area between two curves 8.1 d. Volumes of revolution 8.2, 8.3 e. The Second Fundamental Theorem 7.6 6. Logs and Exponents a. Antiderivative of 1/x 4.4 b. Properties of ln(x) 4.1, 4.4, 4.2 c. Logarithmic differentiation 4.3 d. Function inverses 4.1 e. The exponential function 4.2, 4.4 f. Properties of ex 4.1, 4.2, 4.4 g. Loga and ax 4.2, 4.4 h. Graphs of exponential and log functions 4.2 i. Exponential growth 10.3 7. Inverse Trigonometric Functions a. Graphs, domains, ranges 4.5 b. Triangle computations 4.5 c. Derivatives 4.5 8. More Integration Rules a. Integrals resulting in inverse trig. functions 9.3 b. Integration by parts 9.2 c. Integrals of sin2(x) and cos2(x) 9.2 9. Improper Integrals a. Convergence and divergence 9.8 b. Integrals over an infinite region 9.8 c. Integrals over an open interval 9.8 10. L'Hôpital's rule a. Procedure 4.7 b. Iterated procedure 4.7 c. Other indeterminate forms 4.6

See the course calendar for details concerning exams and quizzes.

 Math 12 - 2 (Winter 2000) web pages Created: 05 Mar 2000 Last modified: 05 Mar 2000 22:11:02 Comments to: `dpvc@union.edu`