Calculus 1 Math 2413 spring 2014 Department of Mathematics Texas A&M University-Commerce 4 hours, 4.0 Credits,
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1 Calculus 1 Math 2413 spring 2014 Department of Mathematics Texas A&M University-Commerce 4 hours, 4.0 Credits, Name: Dr. Derege H. Mussa Office: Bin 320 Phone: Derege.Mussa@tamuc.edu Course Description: This is a one semester introduction to differential and integral calculus, suitable for all students majoring in Science or Mathematics, or any other course of study requiring calculus. Goals: The student will learn about functions of one variable, including the concepts of limit, continuity and the derivatives. The students will be able to compute derivatives of various functions such as polynomials, rational functions, trigonometric functions, exponential and logarithm functions, and inverse trigonometric functions. The student will learn the Mean value Theorem and the Intermediate value Theorem. These concepts will be applied by the student to various problems involving related rates, curve sketching and optimization, and linear approximation. The student will learn about antidifferentiation and the Riemann integral, and will be able to compute Riemann integrals of some simple functions using the Fundamental Theorem of Calculus. Finally, the student will apply these techniques to computing areas. Learning out comes Upon the successful completion of the course, Students will:. Develop solutions for tangent and area problems using the concept of limits, derivatives, and integrals..draw graphs of algebraic and transcendental functions considering limits, continuity, and differentiability at a point.. Determine whether a function is continuous and/or differentiable at a point using limits.
2 .Use differentiation rules to differentiate algebraic and transcendental functions..identify appropriate calculus concepts and techniques to provide mathematical models of real world situations and determine solutions to applied problems..evaluate definite integrals using Fundamental of calculus..articulate the relationship between derivatives and integrals using the Fundamental Theorem of Calculus. Prerequisites: Completion of Math 142 or two years of high school algebra and trigonometry. Textbook: Single variable calculus, 7 th Edition, with webassign, James Stewart, Cengage Publishing. Topics Covered: Chapter 1: Functions 1.4 The Tangent and Velocity problems 1.5 The Limit of a Function 1.6 Calculating Limits using the Limit Laws 1.7 Precise definition of limits 1.8 Continuity Chapter 2: 2.1 Derivatives and Rates of Change 2.2 The Derivatives as a function 2.3 Differentiation Formula 2.4 Derivatives of Trigonometric Functions 2.5 The Chain Rule 2.6 Implicit Differentiation 2.7 Rates of change in the Natural and Social Sciences
3 2.8 Related areas 2.9 Linear Approximation and Differentials Chapter 3: 3.1 Maximum and Minimum values 3.2 The Mean Value Theorem 3.3 How Derivatives affect the shape of a graph 3.4 Limits at Infinity; Horizontal Asymptote 3.5 Summary of curve sketching 3.6 Graphing with calculus and calculator 3.7 optimization problems 3.8 Newton s Method 3.9 Antiderivatives Chapter 4: 4.1 Areas and Distances 4.2 The Definite Integral 4.3 The Fundamental Theorem of Calculus 4.4 Indefinite Integrals and the Net Change Theorem 4.5 The Substitution Rule Chapter 5: 5.1Areas between Curves Chapter 6: 6.2 Derivatives of Polynomials and Exponential Functions 6.3 Logarithmic function
4 6.4 Derivatives of Logarithm Functions 6.5 Exponential Growth and Decay 6.8 Indeterminate forms and L Hospital s Rule Homework: Homework will be assigned on a regular basis and will count 10% of your grade. We will use WebAssign, an online homework system. Exams and Grades: There will be four exams and a cumulative final exam. Your final grade will be determined by 90% of your average on the exams plus your home work. The final exam will be worth two of the other exams. Your lowest exam grade will be dropped. (If the final is the lowest grade it will be counted as one exam). If you miss an exam that will count as your lowest grade so it will be dropped. Exam 1: Exam 2: Exam 3: Grade: A B C D Below 60 F Resources/Equipment: TI-83/84 (some are available for rent in the Math Department office) Class Schedule:
5 TR 11:00-11:50 am Academic Dishonesty: Texas A&M University Commerce has explicit rules and regulations governing academic dishonesty and academic misconduct. These policies are stated in details in the student s Guide Handbook. Each students is expected to read this document and abide by the contained polices. These university polices will be followed in class. The minimum penalty an act of academic dishonesty will be a grade of 0 on the examination or homework assignments. Students with Disability: The American with Disability Act (ADA) is a federal anti-discrimination statute that provides comprehensive civil rights protection for persons with disabilities. Among other things, this legislation requires that all students with disabilities be guaranteed a learning environment that provides for reasonable accommodation of their disabilities. If you have a disability requiring an accommodation. please contact: Office of Student Disability Resources and Services Texas A&M University Commerce Gee Library Room 132 Phone or Fax studentdisabilityservices@tamuc.edu
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