WEEK #10:
Integrals
Integration by Parts, Denition and Application of
Goals:
Integration by Parts
Riemann Sums
Denite Integrals
Fundamental Theorem of Calculus
Textbook reading for Week #10: Read Sections 4.3, 4.4, 4.5
2
Integration by Parts
From Sect
WEEK #11:
Integral Applications, Improper Integrals
Goals:
Applications of Integration
Improper Integrals
Textbook reading for Week #11: Read Sections 4.6, 4.7
2
Applications of Denite Integrals
From Section 4.6
This week, we will be looking some simple
WEEK #7:
Newtons Method, Limits at , LHopitals Rule,
Leading Behaviour
Goals:
Newtons Method
Evaluating innite limits
Relative rates of various function families
Simplifying sketches of functions by studying leading behaviour
Textbook reading for Week
WEEK #8:
Stability, Logistic Model, Breathing Reprise
Goals:
Stability of Equilibria
More Complex Dynamics
Logistic Model
Further Analysis of Breathing Model
Textbook reading for Week #8: Read Sections 3.1, 3.2, 3.9
2
Return to Discrete-Time Dynamical
WEEK #12: Convergence and Applications of Improper Integrals
Goals:
Convergence of Improper Integrals
Applications of Improper Integrals
Textbook reading for Week #12: Read Sections 4.7
2
Convergence of Improper Integrals
From Section 4.7
Using Leading
WEEK #2: Cobwebbing, Equilibria, Exponentials and Logarithms
Goals:
Analyze Discrete-Time Dynamical Systems
Logs and Exponentials
Textbook reading for Week #2: Read Sections 1.61.7
2
Graphical Analysis
To prepare for this topic, you should read Section
WEEK #5:
Trig Functions, Optimization
Goals:
Trigonometric functions and their derivatives
Optimization
Textbook reading for Week #5: Read Sections 1.8, 2.10, 3.3
2
Trigonometric Functions
From Section 1.8
There are two fundamental interpretations of th
WEEK #4:
Review of Derivatives
Goals:
Review the interpretation and rules of derivatives.
Textbook reading for Week #4: Read Sections 2.1, 2.2, 2.4-2.6, 2.8, 2.9
2
Derivatives are covered in the Grade 12 Ontario curriculum. While they will be
reviewed he
WEEK #6: Optimization, Linear Approximations, Taylor Polynomials
Goals:
Non-traditional Optimization
Tangent Line Formulas and Linear Approximations
Taylor Polynomials
Textbook reading for Week #6: Read Sections 3.3, 3.7
2
Optimizing Rate of Collection
WEEK #3:
Lung Model, Stability of Equilibria
Goals:
Introduce iterative model building for the lung.
Introduce a competition model for bacteria.
Develop criteria for classifying the stability of equilibria.
Textbook reading for Week #1: Read Sections 1