19B Notes and Practice Materials

Addition and Multiplication Principles of Counting (Sec 7.1)   Solutions 

Permutations and Combinations (Sec 7.2)   Solutions 

Probability and Counting Techniques (Sec 8.4)   Solutions 

Random Variables and Distributions   Solutions 

Bernoulli Trials and Binomial Random Variables   Solutions 

Intro to Measures of Central Tendency and Dispersion 

Measures of Central Tendency (Sec 9.3)  Solutions 

Measures of Dispersion (Sec 9.4) Solutions *Mistake - Variance on #1 should be 29

Midterm 1 Review Problems (*from textbook) Solutions 

Systems of Linear Equations (Sec 4.1, 4.3)     Solutions 

    Using Matrices to Solve Systems of Linear Equations (Sec 4.2) Solutions 

    Matrix Algebra (Sec 5.1, 5.2) 

Matrix Equations and Inverses (Sec 5.3) 

More Examples of Matrix Equations and Inverses (Sec 5.3)    Solutions 

Game Theory (Sec 5.4)    Textbook Examples 

Game Theory (One or Two Fingers, Rock Paper Scissors) 

Optimal Strategy for Rock Paper Scissors and One Finger Two Fingers 

Game Theory (More Textbook Examples)     Solutions  *Note:  Error in #3 solution, but answer is correct!

More Game Theory Practice 

Input-Output Models 

Input-Output Models (Book Examples) Solutions 

Solving Linear Programming Problems Graphically (Sec 6.2) Solutions 

Linear Programming Applications Solutions 

The Simplex Method (Sec 6.3) 

Simplex Method Examples   Solutions 

More Simplex Method Examples (Standard Maximization) Solutions 

The Simplex Method for Non-Standard Optimization (Sec 6.4) Solutions 

The Simplex Method and Duality (Sec 6.5)     Solutions 

Midterm 2 Review Problems Solutions 

Antiderivatives and the Indefinite Integral 

The Indefinite Integral (Applications) Solutions 

The Substitution Method (Sec 13.2) 

Substitution Application Problems Solutions 

Riemann Sums and the Definite Integral (Sec 13.3) Solutions 

The Fundamental Theorem of Calculus (Sec 13.4) 

FTC Application Problems  Solutions 

More Definite Integrals and Area 

Integration By Parts (Sec 14.1) 

IBP (Applications) Solutions 

Integrals Involving Absolute Value 

Area Between Two Curves (Sec 14.2) 

More Area Problems 

Area Between Two Curves (Applications) 

Averages and Moving Averages (Sec 14.3) Solutions 

    Midterm 3 Review Problems Solutions 

Consumers' and Producers' Surplus, Continuous Revenue Streams Solutions 

Improper Integrals 

Improper Integrals (Applications)   Solutions 

Final Review Problems (Prof. Tav)