Math 3B Course Description

This is a general description of the nature of the course; consult your instructor for specifics

Math 3B is the second course of a two quarter sequence in Differential and Integral Calculus. Homework is typically done online. Consult your instructor about whether a specific textbook will be required.

3B covers about four chapters in a typical textbook. Times given below are approximate and do not include exams. You may, if you wish, do 'Techniques of Integration' immediately after 'Substitution Rule', so all techniques are done in the middle of the course and the applications are done last. This gives a natural way to split the material between two midterms and a final.

Chapters & Topics

4. Applications of Differentiation (continued from 3A) (~ 1 lecture)
     Antiderivatives

5. Integrals (~ 2.5 weeks)
     The Net Change Theorem is the key idea at the level the students can grasp.

6. Applications of Integration (~ 2.5 weeks)
     In sections which emphasize computation of geometric quantities, area or volume, it is a good idea to remind students that these quantities are not intrinsically interesting. It is what they represent (based on the Net Change Theorem) that matters.
    6.1 - 6.5

7. Techniques of Integration (~ 2 weeks)
     This syllabus de-emphasizes the number of different techniques of integration covered in order to allow time for applications. Because of this, we emphasize accuracy of solutions for those techniques which are covered. Students should be taught to take derivatives to see their antiderivative is correct.
     Integration by Parts
     Partial Fractions (Cover the easiest cases only, distinct linear factors or a single irreducible quadratic factor.)
     Tables
     Approximate Integration (optional)
     Improper Integrals

8. Further Applications (~ 2 weeks)
    Arc Length (This is a good place to remind students of the 2nd interpretation of the Fundamental Theorem of Calculus: if an elementary antiderivative can not be found, the definite integral defines a new function where the variable is the upper limit of integration.)
     Area of revolution
     Applications to Physics and Engineering