Students will use appropriate models and quantitative methods to analyze data, explore relationships among variables, and find missing information.

Transcription

1 Master Syllabus and Course Content MATH 2261 Calculus I Georgia Highlands College Updated for Fall 2017 Course Description: Mathematics 2261: Calculus I Prerequisite: MATH 1113 with a grade of C or better This course includes a study of functions, limits, derivatives, continuity, the chain rule, implicit differentiation, related rates, differentials, local extrema, graphing techniques, monotonicity, concavity, m ax-min applications, infinite limits, the mean value theorem, antiderivatives, differential equations, sigma notation, the definite integral and areas in the plane. Student Learning Outcomes: Goals: Students will interpret and apply mathematical information, concepts, and principles embedded in verbal, numerical, graphical, and symbolic Students will use appropriate models and quantitative methods to analyze data, explore relationships among variables, and find missing information. Student Learning Outcomes 1 : Students will be able to solve equations. Students will be able to solve inequalities. Students will be able to graph functions. Students will be able to interpret information presented graphically. Students will be able to express numbers appropriately in a variety of ways based on context. Students will be able to rewrite algebraic expressions appropriately in a variety of ways based on context. Students will be able to use set notation in context. 1 The first twelve outcomes listed correspond to the student learning outcomes approved to support the general education goals related to mathematics.

2 Page 2 of 5 Students will be able to calculate rates of change using multiple Students will be able to interpret rates of change using multiple Students will be able to model scenarios or data mathematically to solve quantitative problems. Students will be able to use technology appropriately. Students will be able to apply logical, mathematical reasoning. Students will be able to calculate and interpret the meaning of limits. Topics Covered: Limits o Techniques for computing limits o Infinite Limits o Limits at Infinity Continuity Difference quotients and the definition of derivative Differentiation Rule o Product, Quotient and Chain Rules Derivatives of trigonometric functions Implicit Differentiation o Related Rate Applications Derivatives of exponential and logarithmic functions Applications of the derivative o Maximum and minimum problems o Optimization o Linear approximation and introduction to differentials Mean Value Theorem L Hopital s Rule Antidifferentiation Approximating area under curves Definite Integrals Fundamental Theorem of Calculus

3 Page 3 of 5 Course Materials: Textbook: Calculus I: Early Transcendental Functions, 6th Enhanced Edition, Larson and Edwards Textbook packaged with WebAssign ISBN: (WebAssign Printed Access Card, Multi-Term from Cengage) Technology: Enhanced WebAssign TI-83/TI-84 or equivalent graphing calculator is required Suggested Course Content: Chapter 1 Preparation for Calculus 1.3 Functions and Their Graphs 1.5 Inverse Functions 1.6 Exponential and Log Functions Chapter 2 Limits and Their Properties 2.1 A Preview of Calculus 2.2 Finding Limits Graphically and Numerically 2.3 Evaluating Limits Analytically 2.4 Continuity and One-sided Limits 2.5 Infinite Limits 4.5 Limits at Infinity Chapter 3 Differentiation 3.1 The Derivative and the Tangent Line Problem 3.2 Basic Differentiation Rules (introduces derivatives of sin, cos, and e^x functions) and Rates of Change 3.3 The Product and Quotient Rule and Higher-Order Derivatives 3.4 The Chain Rule (introduces derivatives of ln, log, and a^x functions) 3.5 Implicit Differentiation 3.6 Derivatives of Inverse Functions(optional) 3.7 Related Rates

4 Page 4 of 5 Chapter 4 Application of Differentiation 4.1 Extrema on the Interval 4.2 Roll s Theorem and Mean Value Theorem 4.3 Increasing and Decreasing Functions and the First Derivative Test 4.4 Concavity and the Second Derivative Test 4.6 A Summary of Curve Sketching 4.7 Optimization Problems 4.8 Differentials 8.7 L Hopital s Rule (optional; can be covered in Calc II) Chapter 5 Integration 5.1 Antiderivatives and Indefinite Integration 5.2 Area 5.3 Riemann Sums and Definite Integral (if time permits) Notes: The worked out solutions are free at CalcChat.com. These come with free live tutorial help. At LarsonCalculus.com, students can watch a video presentation of each lesson. These videos are by Dana Mosely. Also at LarsonCalculus.com, co-author Bruce Edwards presents a video discussion of the proof of each theorem. Suggested Weekly Outline: Week Topics Week 1 Week 2 Week 3 Week Functions and Their Graphs 1.5 Inverse Functions 1.6 Exponential and Log Functions 2.1 A Preview of Calculus 2.2 Finding Limits Graphically and Numerically 2.3 Evaluating Limits Analytically 2.4 Continuity and One-Sided Limits 2.5 Infinite Limits 4.5 Limits at Infinity

5 Page 5 of 5 Week Week 5 Week 6 Week 7 Week 8 Week 9 Week 10 Topics Test Basic Differentiation Rules & R. O.C. 3.3 Product & Quotient Rule; H.O.D. 3.4 Chain Rule 3.5 Implicit Differentiation 3.7 Related Rates Catch-Up / Review Test2 4.1 Extrema on an Interval 4.2 Rolls and the Mean Value Theorem 4.7 Optimization Problems 4.8 Differentials 8.7 L Hopital s Rule Week 11 Test3 5.1 Antiderivatives Week Antiderivatives (continued) 5.1 Area Week 13 Week Riemann Sums Test 4 Review for the Final / catch-up Week 15 Review for the Final/catch-up