Science:Math Exam Resources/Courses/MATH102/Syllabus

Cell size: volume, area. Power functions
Power functions (cont). Sketching simple polynomials (y=x^3-ax)
Sketching simple polynomials (cont). Rational functions, Michaelis-Menten and Hill functions, “limits” at infinity
Average rate of change and secant lines. Definition of the derivative. Instantaneous rate of change
Limits and continuity, examples. One example of computing derivative of y=ct2 from the definition
Derivatives: analytic, and geometric (zoom in on a point). Sketching f′(x) given f(x) (intro)
Derivatives (cont): computational (spreadsheet example in class). More examples of sketching f′(x) given f(x) (intro)
Rules of differentiation: Product and quotient rules. Antiderivatives of power functions. Application to falling ball, motion of Listeria. Sketching f(x) given f′(x) (intro using polynomial)
Tangent lines and linear approximation
Introduction to Newton’s method. Sketching the graph of a function using calculus tools: increasing, decreasing, critical points
Sketching the graph of a function using calculus tools (cont): concavity and inflection points
Putting it all together - sketching
Finish sketching functions. Introduce simple optimization problem(s)
More optimization examples including those with a constraint and those on bounded intervals. Distinction between absolute (global) and local minima and maxima
Kepler's Wedding - A wine optimization problem
Optimal Foraging
Least Squares - finding the mean of a data set
Least Squares - finding the best fitting line y=ax through a set of data points
Chain Rule: examples, applications to optimization problems
More Chain Rule: Related Rates and Implicit differentiation
Exponential functions: intro and motivation, derivative of exponential functions
Inverse functions and logarithm, applications of logs
Exponential growth and decay, intro to differential equations, population growth and/or other examples
Solving differential equations of the type dy/dt=a−by
Newton's Law of Cooling (Murder Mystery example)
Complete and/or review above topics
Solving differential equations approximately using Euler's Method
Introduction to nonlinear ODEs, qualitative analysis
Slope fields with logistic equation as example
State-space diagrams and examples (logistic)
Disease dynamics
Review of differential equations and/or complete above topics
Introduction to Trigonometric Functions
Trigonometric Functions and cyclic processes, phase, amplitude, etc. (fitting a sin or cos to a cyclic process), Inverse trig functions
Derivatives of trig functions, related rates examples
The Escape Response and inverse trig functions
Second order ODEs. Complete and/or review trig