SECTION ASSIGNMENT SHEET |
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1 Preview and Review |
1.1 |
Preliminaries |
1.2 |
Elementary Functions |
1.3 |
Graphing |
1.4 |
Review Problems |
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2 Discrete Time Models, Sequences and Difference
Equations |
2.1 |
Exponential Growth and Decay |
2.2 |
Sequences |
2.3 |
More Population Models |
2.4 |
Review Problems |
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3 Limits and Continuity |
3.1 |
Limits |
3.2 |
Continuity |
3.3 |
Limits at Infinity |
3.4 |
The Sandwich Theorem and Some
Trigonometric Limits |
3.5 |
Properties of Continuous
Functions |
3.6 |
Formal Definition of Limits |
3.7 |
Review Problems |
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4 Differentiation |
4.1 |
Formal Definition of the
Derivative |
4.2 |
The Power Rule, the Basic Rules
of Differentiation, and the Derivatives of Polynomials |
4.3 |
Product Rule and Quotient Rules |
4.4 |
The Chain Rule and Higher
Derivatives |
4.5 |
Derivatives of Trigonometric
Functions |
4.6 |
Derivatives of Exponential
Functions |
4.7 |
Derivatives of Inverse and
Logarithmic Functions |
4.8 |
Approximation and Local
Linearity |
4.9 |
Review Problems |
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5 Applications of Differentiation |
5.1 |
Extrema and the Mean Value
Theorem |
5.2 |
Monotonicity and Concavity |
5.3 |
Extrema, Inflection Points and
Graphing |
5.4 |
Optimization |
5.5 |
L'Hospital's Rule |
5.6 |
Difference Equations: Stability |
5.7 |
Numerical Methods |
5.8 |
Antiderivatives |
5.9 |
Review Problems |
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6 Integration |
6.1 |
The Definite Integral |
6.2 |
The Fundamental Theorem of
Calculus |
6.3 |
Applications of Integration |
6.4 |
Review Problems |
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7 Integration Techniques and Computational Methods |
7.1 |
The Substitution Rule |
7.2 |
Integration by Parts |
7.3 |
Practicing Integration and
Partial Fractions |
7.4 |
Improper Integrals |
7.5 |
Numerical Integration |
7.6 |
Tables of Integrals |
7.7 |
The Taylor Approximation |
7.8 |
Review Problems |
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8 Differential Equations |
8.1 |
Solving Differential Equations |
8.2 |
Equilibria and Their Stability |
8.3 |
Systems of Autonomous Equations |
8.4 |
Review Problems |
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9 Linear Algebra and Analytic Geometry |
9.1 |
Linear Systems |
9.2 |
Matrices |
9.3 |
Linear Maps, Eigenvectors and
Eigenvalues |
9.4 |
Analytic Geometry |
9.5 |
Review Problems |
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10 Multivariable Calculus |
10.1 |
Functions of Two or More
Independent Variables |
10.2 |
Limits and Continuity |
10.3 |
Partial Derivatives |
10.4 |
Tangent Planes,
Differentiability, and Linearization |
10.5 |
More About Derivatives |
10.6 |
Applications |
10.7 |
Systems of Difference Equations |
10.8 |
Review Problems |
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11 Systems of Differential Equations |
11.1 |
Linear Systems: Theory |
11.2 |
Linear Systems: Applications |
11.3 |
Nonlinear Autonomous Systems:
Theory |
11.4 |
Nonlinear Systems: Applications |
11.5 |
Review Problems |
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12 Probability and Statistics |
12.1 |
Counting |
12.2 |
What Is Probability? |
12.3 |
Conditional Probability and
Independence |
12.4 |
Discrete Random Variables and
Discrete Distributions |
12.5 |
Continuous Distributions |
12.6 |
Limit Theorems |
12.7 |
Statistical Tools |
12.8 |
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