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1141 M05-09
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Calculus 1
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Week 1
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2.1
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The Tangent and Velocity Problems
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Worksheet 1 (Inverse Trigonometric Functions)
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2.2
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The Limit of a Function
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2.3
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Calculating Limits Using the Limit Laws
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Week 2
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2.5
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Continuity
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Worksheet 2 (The Precise Definition of a Limit)
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2.6
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Limits at Infinity; Horizontal Asymptotes
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2.7
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Derivatives and Rates of Change
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Week 3
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2.8
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The Derivative as a Function
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3.1
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Derivatives of Polynomials and Exponential Functions
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3.2
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The Product and Quotient Rules
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3.3
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Derivatives of Trigonometric Functions
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Week 4
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3.4
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The Chain Rule
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3.5
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Implicit Differentiation
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3.6
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Derivatives of Logarithmic and Inverse Trigonometric Functions
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3.10
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Linear Approximations and Differentials
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Week 5
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4.1
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Maximum and Minimum Values
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Worksheet 3 (Related Rates)
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4.2
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The Mean Value Theorem
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4.3
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What Derivatives Tell Us about the Shape of a Graph
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Week 6
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4.4
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Indeterminate Forms and l'Hospital's Rule
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4.5
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Summary of Curve Sketching
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Week 7
10/13(Mon) Calculus 1 Drop Deadline
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4.7
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Optimization Problems
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4.9
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Antiderivatives (*)
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Week 8
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Buffer
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11/1(Sat) or 11/2(Sun) Exam
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Calculus 2
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Week 9
10/31(Fri) Calculus 2 Withdrawal Deadline
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5.1
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The Area and Distance Problems
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5.2
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The Definite Integral
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5.3
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The Fundamental Theorem of Calculus
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Week 10
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5.4
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Indefinite Integrals and the Net Change Theorem
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Worksheet 1 (Volumes)
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5.5
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The Substitution Rule
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6.1
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Areas Between Curves
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Week 11
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7.1
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Integration by Parts
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7.2
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Trigonometric Integrals
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Week 12
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7.3
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Trigonometric Substitution
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Worksheet 2 (Other Applications)
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7.4
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Integration of Rational Functions by Partial Fractions
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Week 13
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7.5
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Strategy for Integration
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7.8
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Improper Integrals
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Week 14
12/5(Fri) Calculus 2 Drop Deadline
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8.5
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Probability
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9.1
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Modeling with Differential Equations
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Week 15
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9.3
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Separable Equations
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Worksheet 3 (More on Probability)
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9.5
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Linear Equations
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Week 16
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Buffer
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12/20(Sat) or 12/21(Sun) Exam
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1142 M05-09
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Calculus 3
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Week 1
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12.6
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Cylinders and Quadric Surfaces
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Worksheet 1 (Space Curves and Their Tangents)
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14.1
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Functions of Several Variables
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14.2
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Limits and Continuity
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14.3
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Partial Derivatives
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Week 2
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14.4
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Tangent Planes and Linear Approximations
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14.5
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The Chain Rule
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Week 3
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14.6
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Directional Derivatives and the Gradient Vector
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Worksheet 2 (Polar Coordinates)
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14.7
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Maximum and Minimum Values
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Week 4
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14.8
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Lagrange Multipliers
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15.1
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Double Integrals over Rectangles
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Week 5
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15.2
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Double Integrals over General Regions
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15.3
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Double Integrals in Polar Coordinates
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Week 6
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15.6
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Triple Integrals
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Worksheet 3 (Applications of Double Integrals)
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15.7
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Triple Integrals in Cylindrical Coordinates
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15.8
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Triple Integrals in Spherical Coordinates
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Week 7
4/7(Tue) Calculus 3 Drop Deadline
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15.9
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Change of Variables in Multiple Integrals
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Week 8
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Buffer
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4/18(Sat) or 4/19(Sun) Exam
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Calculus 4
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Week 9
4/24(Fri) Calculus 4 Withdrawal Deadline
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16.1
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Vector Fields
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Worksheet 1 (Parametric Surfaces)
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16.2
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Line Integrals
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16.3
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The Fundamental Theorem for Line Integrals
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Week 10
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16.4
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Green's Theorem
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16.5
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Curl and Divergence
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Week 11
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16.6
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Parametric Surfaces and Their Areas
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Worksheet 2 (More on Conservative Fields)
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16.7
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Surface Integrals
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Week 12
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16.8
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Stokes' Theorem
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16.9
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The Divergence Theorem
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11.1
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Sequences (*)
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Week 13
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11.2
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Series
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Worksheet 3 (Convergence Tests)
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11.3
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The Integral Test and Estimates of Sums
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11.4
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The Comparison Tests (Skip the Limit Comparison Test)
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11.5
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Alternating Series and Absolute Convergence
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Week 14
5/29(Fri) Calculus 4 Drop Deadline
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11.6
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The Ratio and Root Tests
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11.8
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Power Series
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11.9
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Representations of Functions as Power Series
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Week 15
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11.10
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Taylor and Maclaurin Series
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Bonus Introduction to Multivariable Taylor Series (*)
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Week 16
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Buffer
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6/13(Sat) or 6/14(Sun) Exam
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