Up: Math 12 Home Page

Math 12 Course Outline:

Section(s)
1. Riemann Sums
a. Examples 5.4, 5.5
b. Sigma Notation 5.4
c. Useful sums 5.4
d. Limits of sums 5.5
2. The Definite Integral
a. Definition and notation 5.6, 5.5
b. Interpretations 5.8 (sort of)
c. Sums, products and inequalities 5.6
d. Integrability 5.6
3. Antiderivatives
a. Definition and notation 5.2
b. Uniqueness 5.2
c. The Fundamental Theorem of Calculus 5.7
d. The indefinite integral 5.2
4. Integration Rules
a. Power, sum, product, quotient rules 5.2
b. Trigonometric rules 5.2
c. Integration by substitution 5.3, 5.8
5. Applications of Integration
a. Linear motion 6.6
b. Area under a curve, signed area 5.5, 6.1
c. Area between two curves 6.1
d. Volumes of revolution 6.2, 6.3
e. The Second Fundamental Theorem 5.9
6. Logs and Exponents
a. Antiderivative of 1/x 7.5
b. Properties of ln(x) 7.5, 7.1, 7.2, 7.3
c. Logarithmic differentiation 7.2
d. Function inverses 7.4
e. The exponential function 7.5, 7.2
f. Properties of ex 7.5, 7.1, 7.2, 7.3
g. Loga and ax 7.1, 7.5
h. Graphs of exponential and log functions 7.3
i. Exponential growth 7.7
7. Inverse Trigonometric Functions
a. Graphs, domains, ranges 8.1
b. Triangle computations 8.1
c. Derivatives 8.2
8. More Integration Rules
a. Integrals resulting in inverse trig. functions 8.2
b. Integration by parts 9.2
c. Integrals of sin2(x) and cos2(x) 9.3
9. Improper Integrals
a. Convergence and divergence 10.1
b. Integrals over an infinite region 10.1
c. Integrals over an open interval 10.1
10. L'Hôpital's rule
a. Procedure 10.2
b. Iterated procedure 10.2
c. Other indeterminate forms 10.3

See the course calendar for details concerning exams and quizzes.


Up: Math 12 Home Page

Comments to: dpvc@union.edu
Created: Mar 24 1998 --- Last modified: Jun 1, 1998 10:27:48 AM