| Topic |
Theory |
Homework |
- elements of set theory
- algebraic skills
- the real line
- real functions
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Adams, R. A. and Essex, C. (2021).Calculus: A Complete Course. 10th ed. Toronto: Pearson
- P1: The Real Numbers and the Real Line
- P2: Cartesian Coordinates in the Plane
- P3: Graphs of Quadratic Equations
- §8.1: Conics (Optional)
- P4: Functions and Their Graphs
- P5: Combining Functions to Make New Functions
- P6: Polynomials and Rational Functions
- P7: The Trigonometric Functions
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Adams, R. A. and Essex, C. (2021). Calculus: A Complete Course. 10th ed. Toronto: Pearson
- P1: 3, 6, 7, 9, 17, 19, 25, 31, 39, 41
- P2: 9, 11,38, 41, 49
- P3: 7, 15, 19, 35, 39, 51
- §8.1: 1, 3, 5, 7, 11 (Optional)
- P4: 6, 7, 13, 22, 37
- P5: 2, 6, 7f, 7h, 9, 13, 15, 23, 25, 27a, 33
- P6: 5, 9, 16, 20, 23, 24
- P7: 5, 9, 22, 24, 25, 31, 37, 47, 50
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- single-variable functions
- limits
- continuity
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- § 1.2: Limits of Functions
- § 1.3: Limits at Infinity and Infinite Limits
- § 1.4: Continuity
- § 1.5: The Formal Definition of Limit (Optional)
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- § 1.2: 25, 29, 33, 39, 63, 75
- § 1.3: 9, 13, 21, 29, 31
- § 1.4: 1, 9, 15, 17, 30
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- differentiation
- the chain rule
- the mean-value theorem
- implicit differentiation
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- § 2.1: Tangent Lines and Their Slopes
- § 2.2: The Derivative
- § 2.3: Differentiation Rules
- § 2.4: The Chain Rule
- § 2.5: Derivatives of Trigonometric Functions
- § 2.6: Higher-Order Derivatives
- § 2.8 The Mean-Value Theorem
- § 2.9 Implicit Differentiation
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- § 2.1: 15, 16, 24
- § 2.2: 2, 6, 11, 15, 27, 37,38
- § 2.3: 17, 23, 39, 41
- § 2.4: 14, 16, 23, 33, 40
- § 2.5: 32, 41, 53, 56, 58
- § 2.6: 7, 11, 28
- § 2.8: 3, 4, 7, 18
- § 2.9: 3, 5, 11, 17, 21, 25, 29
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- applications of differentiation
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- § 4.4 Extreme Values
- § 4.5 Concavity and Inflections
- § 4.8 Extreme-Value Problems
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- § 4.4: 17, 31, 35
- § 4.5: 9, 10, 27, 36
- § 4.8: 17, 28
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- inverse functions
- transendental functions
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- § 3.1 Inverse Functions
- § 3.2 Exponential and Logarithmic Functions
- § 3.3 The Natural Logarithm and
Exponential Functions
- § 3.4 Growth and Decay
- § 3.5 The Inverse Trigonometric Functions
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- § 3.1: 9, 12, 19, 23, 28
- § 3.2: 11, 25, 27, 30, 33
- § 3.3: 17, 29, 39, 47, 53, 55, 65
- § 3.4: 1, 2, 3, 4, 5, 6, 7, 8
- § 3.5: 15, 19, 43
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- linear approximations
- Taylor expansion
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- § 4.9 Linear Approximations
- § 4.10 Taylor Polynomials
- § 4.3 Indeterminate Forms
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- § 4.9: 11, 15, 29
- § 4.10: 5, 7, 21, 26
- § 4.3: 2, 6, 8, 9, 13, 20, 23, 26, 27
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- The Riemann Integral
- definite integration
- indefinite integration
- integration techniques
- improper integrals
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- § 2.10: Antiderivatives and Initial Value Problems
- § 5.1 Sums and Sigma Notation
- § 5.2 Areas as Limits of Sums
- § 5.3 The Definite Integral
- § 5.4 Properties of the Definite Integral
- § 5.5 The Fundamental Theorem of Calculus
- § 5.6 The Method of Substitution
- § 5.7 Areas of Plane Regions
- Appendix IV: The Riemann Integral (Optional)
- § 6.1 Integration by Parts
- § 6.2 Integrals of Rational Functions
- § 6.5 Improper Integrals
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- § 2.10: 1, 3, 5, 7, 9, 11, 13
- § 5.4: 2, 5, 25, 29, 33
- § 5.5: 33, 36, 39, 42, 44, 46
- § 5.6: 8, 17, 23, 26, 35, 43
- § 5.7: 3, 5, 11
- § 6.1: 6, 8, 9, 14, 21, 23, 36
- § 6.2: 5, 9, 11
- § 6.5: 7, 15, 19, 20
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- first-order differential equations
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- § 2.10: Antiderivatives and Initial Value Problems
- § 7.9 First-Order Differential Equations
- § 3.4 Growth and Decay
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- § 2.10: 27, 31, 37
- § 7.9: 3, 8, 14, 15, 18, 21, 28, 29
- § 3.4: 9, 10, 11, 12, 25, 32, 33
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- vectors, lines and planes
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- § 10.1: Analytic Geometry in Three Dimensions
- § 10.2: Vectors
- § 10.3: The Cross Product in 3-Space
- § 10.4: Planes and Lines
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- § 10.1: 3, 7, 11, 15, 17, 31
- § 10.2: 5, 10, 15, 29, 30
- § 10.3: 1, 3, 5, 7-11, 15
- § 10.4: 3, 7, 11, 15, 17, 19, 27, 29
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