Department of Mathematics Syllabus
This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.
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|1-3||1.1-1.5||Preliminaries: Elementary functions and graphing.
Include one full lecture on transformation of functions, log transforms, and log-log/semi-log plot
|4-5||1.6, 2.1||Sequences, discrete-time models, and limits of sequences|
|6-8||2.2-2.5||Limits of functions: limit laws, limits at infinity, algebraic methods, continuity|
|9||3.1||Derivatives as rates of change, tangent lines|
|10-12||3.2, 3.3||Derivatives as functions, differentiability, higher derivatives, power rule, basic differentiation rules, derivatives of exponential functions, derivatives of sine and cosine|
|13||3.4||Product and quotient rules|
|14-15||3.5||Chain rule, implicit differentiation, related rates|
|16||3.6||Exponential growth and decay|
|17||3.7||Derivatives of inverse and logarithmic functions|
|18||3.8||Linear approximation (Optional: Newton's method, Taylor polynomials)|
|20||4.2||Monotonicity and concavity (Optional: Mean Value Theorem)|
|21||4.2||Graphing – Examples including sigmoidal curves|
|25||4.5||Stability of fixed points in recursions|
|26-27||Use remaining lectures as buffer for material above and/or to cover optional material in 3.8|
This course covers chapters 1-4: limits and derivatives; applications of differentiation in biology; recursions.
- use appropriate transformations to find power law and exponential relationships,
- create discrete-time models of biological phenomena and analyze their behavior,
- understand the meaning of limits and derivatives of functions,
- calculate limits and derivatives of functions using appropriate techniques,
- interpret derivatives in a biological context, including ecological, physiological, and pharmacological models,
- approximate functions and bound error using derivatives,
- apply problem-solving skills and knowledge of calculus to solve related rates and optimization problems, and
- use derivatives to predict the behavior of and graph functions.