Math 1101 Calculus I
Week 1:Mon |
No Class: Martin Luther King Day | |
Tue |
Course Introduction Brain...Warming...Up... |
Cube Root of -1 Brain Solutions |
Wed |
1.1 Four Ways to Represent a Function | examples Lecture Notes Functional Notation |
Fri |
1.2 Mathematical Models: Catalog of Essential Functions | examples The Twelve Basic Functions 1.2.25.nb (MMA example) |
Week 2:
Mon |
1.3 New Functions from Old Functions | examples |
Tue |
Mathematica Introduction: Work through MMA Basics and MMA Introduction |
Do examples in Section 1.4 using Mathematica |
Wed |
1.5 Exponential Functions | examples |
Fri |
1.6 Inverse Functions and Logarithms | examples |
Week 3:
Mon |
1.6 Inverse Functions and Logarithms | |
Tue |
Test 1: 1.1-1.3, 1.5, 1.6 | Review Notes for Chapter 1 |
Wed |
2.1 The Tangent and Velocity Problems | examples Animation of Secant Approaching Tangent |
Fri |
2.2 The Limit of a Function | examples |
Week 4:
Mon |
2.3 Calculating Limits Using the Limit Laws | examples MMA Practice |
Tue |
2.5 Continuity | examples |
Wed |
2.6 Limits at Infinity; Horizontal Asymptotes | examples |
Fri |
2.7 Derivatives and Rates of Change | examples MMA Practice Graphical picture of derivative |
Week 5:
Mon |
2.8 The Derivative as a Function Mathematica Notebook |
examples A function with a sharp corner |
Tue |
Test 2: 2.1-2.3, 2.5-2.8 | Notes | review problems | Concept Map |
Wed |
3.1 Derivatives of Polynomials and Exponential Functions | examples Notes: The Other Derivative Proofs |
Fri |
3.2 The Product and Quotient Rules | examples Examples from the lecture MMA Derivative Syntax |
Week 6:
Mon |
More on 3.1 and 3.2: Derivative Rules and Proofs | |
Tue |
3.3 Derivatives of Trigonometric Functions | examples Trigonometry Review MMA File |
Wed |
3.4 The Chain Rule | examples MMA Practice Chain Rule: Graphical Interpretation Derivative Calculator on Web |
Fri |
3.5 Implicit Differentiation | examples |
Week 7:
Mon |
3.6 Derivatives of Logarithmic Functions | examples MMA Practice |
Tue |
3.7 Rates of Change in Natural and Social Sciences | examples FishFarm.nb (MMA file) Sounds.nb (MMA file) |
Wed |
3.9 Related Rates | Examples from the lecture |
Fri |
3.9 Related Rates | examples |
Week 8:
Mon |
3.10 Linear Approximation and Differentials | examples (questions like these will not be on the test, but they give you an idea of the power of the techniques we learned in Chapter 3) |
Tue |
Test 3: 3.1-3.7,3.9 | review problems | Concept Map |
Wed |
4.1 Maximum and Minimum Values | examples |
Fri |
4.2 The Mean Value Theorem |
Week 9:
Mon |
4.3 How Derivatives Affect the Shape of a Graph | examples |
Tue |
4.4 Indeterminate Forms and l'Hospital's Rule | examples Application in Biology (paragraph three in Model Implications) |
Wed |
4.4 Indeterminate Forms and l'Hospital's Rule | |
Fri |
4.5 Summary of Curve Sketching |
Week 10:
Mon |
4.7 Optimization | examples MMA Practice Examples from lecture |
Tue |
4.7 Optimization Problems | |
Wed |
4.8 Newton's Method | examples (MMA) Mathematica (Newtons Method) |
Fri |
4.9 Antiderivatives | examples |
Week 11:
Mon |
Review | |
Tue |
Test 4: 4.1--4.5, 4.7, 4.8 | review problems |
Wed |
5.1 Areas and Distances | examples MMA |
Fri |
5.2 The Definite Integral | examples |
Week 12:
Mon |
5.2 The Definite Integral | Estimating Areas (MMA file) |
Tue |
5.3 The Fundamental Theorem of Calculus | examples MMA Practice |
Wed |
5.4 Indefinite Integrals and the Net Change Theorem | examples How to Remember the Basic Integrals Examples from the lecture Animations of Position and Velocity |
Fri |
5.5 The Substitution Rule | examples |
Week 13:
Mon |
5.5 The Substitution Rule | Examples from the lecture |
Tue |
Test 5: 5.1-5.5 | review problems | Glossary |
Wed |
10.1 Curves Defined by Parametric Equations 10.2 Tangents and Areas |
examples Mathematica (parametric functions) |
Fri |
Handout: Surfaces & Traces MMA file |
MMA (Surfaces and traces) |
Week 14:
Mon |
Handout: Space Curves & Contour Plots |
MMA (space curves and contour plots) Mathematica (intersections, contour plots) Software using Surface Intersection Weather Pattern Contour Plots Topographical Maps |
Tue |
Handout: Partial Derivatives | MMA (partial derivatives) tangent line animations | MMA |
Wed |
Handout: Partial Derivatives | |
Fri |
Handout: Extrema Extrema Examples |
MMA (extrema) |
Week 15:
Mon |
Review, deeper look at some topics | |
Tue |
Review, deeper look at some topics | Glossary Quiz | Solution |
Wed |
Review, deeper look at some topics | |
Fri |
Review, deeper look at some topics |