17C New Book (Stewart)

*Videos for the notes below are here

  Level Curves and 3D Graphing 

 Body Mass Index and Infectious Disease Models 

  Domain and Range Video 

  Limits and Continuity

 How To Show An Indeterminate Limit Exists

 Partial Derivatives

 Tangent Planes and Linearizations

 The Chain Rule Ohm's Law Example 

 Directional Derivatives  *Note: On page 1, the dot product should be (a)(c)+(b)(d)

 Properties of the Gradient

 Infectious Disease Model (Application of Directional Derivatives)

 Finding Local (Relative) Extrema

 Absolute Extrema on a Closed Boundary

 Multivariable Optimization Problems

 Biology Example of Finding Extrema (9.6, 40)

How To Identify Max, Min and Saddle Points From a Gradient Vector Field 

A Failure of Clairaut's Theorem 

 Double Integrals   *Note:  For example 1b), the right and left bounds are backwards!

Midterm 1 Review Problems *From old 17 Calc book, but most problems are relevant. Solutions 

 Intro to Linear Systems of DEs

 Solving a Linear System of DEs (Saddle)

 Graphing a Phase Plane (Sink)

Envisioning Eigenlines and Nullclines in a Direction Field 

 Stability Classifications for Real Eigenvalues

 Eulers Formula

 Stability for Linear Systems of DEs with Complex Eigenvalues

Writing the Solution to a Linear System of DE's With Complex Eigenvalues   (Video)

 Direction of Spiral

 Trace-Determinant Method for Classifying Stability

Sec. 10.4, #10 (A Proof) 

 Linear System of DEs Application (10.3, #4)  

 Applications of Linear Systems of DE's

 Solving a Messy Linear System and Another Application Problem

 Solving Nonhomogeneous Linear Systems of DE's

 A Double Compartment (Tank) Problem

 Non-homogeneous Linear System of DEs Application (10.3, 11)

 Gap Dynamics Problem

 Solving 2nd Order Linear DEs

 A Linear System With Repeated Eigenvalues

 Non-Linear Systems of DEs

 Linearization of a Nonlinear System of DE's

 A Predator Prey Model

Interspecific Competition Models 

 Fitzhugh Nagumo Model for Neuron Action Potential

 Midterm 2 Practice Problems (Carlsson)

 Principles of Counting

 More Counting Practice    More Counting Practice (Solutions)

Even More Counting Problems 

12.1, #5 and #50 

Counting With Dividers 

 Using Combinations to Count Poker Hands

 The Multinomial Coefficient and Counting Walks on a Graph (Prof. Carlsson)

 Probability

 Conditional Probability

 Bayes Rule and Testing for Independence Video 

 More Conditional Probability

 Expected Value, Variance, Probability and Cumulative Distributions (Sec. 12.4)

 Mark-Recapture Probability (Chp 12 Review, 23)

 

Final Review (Old Book) Solutions 

Final Review (2) Solutions