Math 266
Calculus with Applications to Biology.
This page contains general information about Math 266A and B. Please contact your instructor for specific information such as assignments, tests, etc.
MATH 266 is a calculus sequence that has been specifically designed to meet the needs of prospective life science majors. The mathematical concepts covered in these courses will be developed in the context of biological questions, and numerous exercises will demonstrate further applications of calculus in the life sciences.
The course has two sections, MATH 266A and B, that roughly correspond to MATH 263A and MATH 263B. The prerequisite for MATH 266A is MATH 115 or placement level 3. Students who successfully complete MATH 266A have the option to take either MATH 266B or MATH 263B, but MATH 263A is not considered a sufficient prerequisite for MATH 266B. Students who successfully complete MATH 266B and who wish to learn more calculus can enroll in MATH 263C.
The textbook is "Calculus for Biology and Medicine" by Claudia Neuhauser, Prentice Hall, second edition. The outlines below talk about "weeks", but not all weeks are necessarily equal. Sometimes the material allotted to one week will require five lectures, and sometimes it can be covered in three sessions.
Topics in Math 266A
| Week |
Section | Topic |
|---|---|---|
| 1 | 1.1 | Preliminaries |
| 1.2 | Elementary functions |
|
| 2 | 1.3 | Graphing |
| 2.1 | Exponential growth and decay |
|
| 3 | 2.2 | Sequences |
| 2.3 | More population models |
|
| 4 | 3.1 | Limits |
| 3.2 | Continuity | |
| 5 | 3.3 | Limits at infinity |
| 3.4 | Sandwich theorem and some trigonometric limits |
|
| 3.5 | Properties of continuous functions |
|
| 6 | 4.1 | Formal definition of the derivative |
| 4.2 | The Power Rule, the basic rules of differentiation, and the derivatives of polynomials | |
| 4.3 | The Product and Quotient Rules, and the derivatives of rational and power functions | |
| 7 | 4.4 | The Chain rule and higher derivatives |
| 4.5 | Derivatives of trigonometric functions |
|
| 4.6 | Derivatives of exponential functions |
|
| 8 | 4.7 | Derivatives of inverse and logarithmic functions |
| 4.8 | Approximation and local linearity | |
| 9 | 5.1 | Extrema and the Mean Value Theorem |
| 5.2 |
Monotonicity and concavity | |
| 5.3 |
Extrema, inflection points, and graphing | |
| 10 |
5.4 |
Optimization |
| 5.5 |
L'Hopital's Rule |
Topics in Math 266B
| Week |
Section | Topic |
|---|---|---|
| 1 | 5.8 | Antiderivatives. |
| 6.1 | The definite integral | |
| 6.2 | The Fundamental Theorem of Calculus. | |
| 2 | 6.3 | Applications of integration |
| 3 | 7.1 | The Substitution Rule |
| 7.2 | Integration by parts | |
| 4 | 7.3 | Practicing integration and partial fractions |
| 7.4 | Improper integrals | |
| 5 | 7.5 | (optional) Numerical Integration |
| 8.1 |
Solving differential equations | |
| 6 | 8.2 | Equillibria and their stability |
| 5.6 | Difference equations: stability |
|
| 7 | 9.1 | Linear systems |
| 9.2 | Matrices | |
| 8 | 9.3 | Linear maps, eigenvectors, eigenvalues |
| 9 | 11.1 | Theory of linear systems of differential equations |
| 10 | 11.2 | Applications of linear systems of differential equations |
| 11.3 | Nonlinear systems of differential equations |
