# Science:Math Exam Resources/Courses/MATH102

 MATH102

## General Course Info

Visit the course main page here.

## Dynamic Course 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

## All Topics in this Course in Alphabetical Order

MER QGH flag, MER QGQ flag, MER QGS flag, MER QGT flag, MER Tag Implicit differentiation---MER QGH flag, MER QGQ flag, MER QGS flag, MER QGT flag, MER Tag Chain rule---MER CH flag, MER CS flag, MER QGQ flag, MER RT flag, MER Tag Newton's method---MER CH flag, MER CS flag, MER QGQ flag, MER RT flag, MER Tag Linear approximation---MER CH flag, MER CS flag, MER QGQ flag, MER RT flag, MER Tag Tangent line---MER CH flag, MER CS flag, MER QGQ flag, MER RT flag, MER Tag Tangent line---MER CH flag, MER CS flag, MER QGQ flag, MER RT flag, MER Tag Tangent line---MER CH flag, MER CS flag, MER QGQ flag, MER RT flag, MER Tag Tangent line---MER CH flag, MER CS flag, MER QGQ flag, MER QGT flag, MER Tag Limit definition of the derivative---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Differentiate (other)---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Quotient rule---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Implicit differentiation, MER Tag Quotient rule---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Tangent line---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Implicit differentiation, MER Tag Tangent line---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Newton's method---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Limit of a rational function---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Limit of a rational function---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Limit of a trigonometric function---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Steady state and equilibrium---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Separation of variables---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Euler's method---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Implicit differentiation---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Asymptote---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Critical points and intervals of increase and decrease---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Concavity---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Critical points and intervals of increase and decrease---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Concavity---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Graphing of a function---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Critical points and intervals of increase and decrease---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Tangent line---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Related rates---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Related rates---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Related rates---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Equations of motion---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Equations of motion---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Equations of motion---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Optimization---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Optimization---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Tangent line---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Limit of a rational function---Candidates for deletion, MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Steady state and equilibrium---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Antiderivative sketching---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Critical points and intervals of increase and decrease---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Discrete probability---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Discrete probability---MER QGH flag, MER QGQ flag, MER QGS flag, MER QGT flag, MER Tag Population dynamics---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Discrete probability---MER QGH flag, MER QGQ flag, MER QGS flag, MER QGT flag, MER Tag Limit definition of the derivative---MER QGH flag, MER QGQ flag, MER QGS flag, MER QGT flag, MER Tag Linear approximation---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Newton's method---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Population dynamics---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Steady state and equilibrium---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Antiderivative sketching---MER QGH flag, MER QGQ flag, MER QGS flag, MER QGT flag, MER Tag Related rates---MER QGH flag, MER QGQ flag, MER QGS flag, MER QGT flag, MER Tag Optimization---MER QGH flag, MER QGQ flag, MER QGS flag, MER QGT flag, MER Tag Concavity---MER QGH flag, MER QGQ flag, MER QGS flag, MER QGT flag, MER Tag Euler's method---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Tangent line---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Linear approximation---MER QGH flag, MER QGQ flag, MER QGS flag, MER QGT flag, MER Tag Steady state and equilibrium---MER QGH flag, MER QGQ flag, MER QGS flag, MER QGT flag, MER Tag Implicit differentiation---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Implicit differentiation---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Critical points and intervals of increase and decrease---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Initial value problem---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Limit definition of the derivative---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Continuity---MER QGH flag, MER QGQ flag, MER QGS flag, MER QGT flag, MER Tag Related rates---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Concavity, MER Tag Critical points and intervals of increase and decrease, MER Tag Graphing of a function---MER QGH flag, MER QGQ flag, MER QGS flag, MER QGT flag, MER Tag Optimization---MER QGQ flag, MER QRH flag, MER RS flag, MER RT flag, MER Tag Tangent line---MER QGQ flag, MER QRH flag, MER RS flag, MER RT flag, MER Tag Continuity---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Exact differential equation---MER QBH flag, MER QBS flag, MER QGQ flag, MER RT flag, MER Tag Exact differential equation---MER QGQ flag, MER QGS flag, MER RH flag, MER RT flag, MER Tag Newton's law of cooling---MER QBH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Newton's method---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Chain rule, MER Tag Critical points and intervals of increase and decrease, MER Tag Product rule---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Population dynamics---MER QBS flag, MER QGH flag, MER QGQ flag, MER RT flag, MER Tag Tangent line---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Euler's method---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Linear approximation---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Related rates---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Implicit differentiation, MER Tag Quotient rule---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Steady state and equilibrium---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Steady state and equilibrium---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Steady state and equilibrium---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Steady state and equilibrium---MER QBH flag, MER QBS flag, MER QGQ flag, MER RT flag, MER Tag Optimization---

Midterm 1: Tuesday, September 30th
Midterm 2: Tuesday, November 4th
Day of final exam: Saturday, December 6th at 3:30pm