Description

This is a second semester course in calculus with applications in biology and life sciences. Credit will be granted for only one of the following: MATH 131 or MATH 141 or MATH 221.

Prerequisites

Math 130 with a C- or better or Math140 with a C- or better

Topics

Integration and Review

FToC review and examples
Area between two curves, numerical integration (Trapezoidal and Simpson's)
Integration by parts, volume
Average value of a function, improper integrals

Linear Algebra

Definition of vectors and matrices
Systems of equations, multiplication of a matrix and a vector
Matrix addition, multiplication, identity matrix, invertible matrices
Linear maps and correspondence to matrix multiplication
Eigenvalues and eigenvectors

Multivariable Calculus

Functions of several variables, derivatives
Computing the derivative, derivatives
Optimization
Double integrals, use for volume under a function, iterated integrals

Differential Equations

Introduction and separable differential equations
First-order linear, Euler's method
Linear systems
Nonlinear systems, phase plane (single equilibrium point)

Probability

Discrete random variables
Continuous random variables, uniform distribution
Exponential and normal random variables
Central Limit Theorem
Inferential statistics

Discrete Dynamics

Inspiration and sequences
Equilibrium and stability, cobwebbing
Population models