# MTH 141 Calculus 1 Syllabus Spring 2017

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2 General Education Areas MTH 141 is a General Education course. The General Education areas satisfied by MTH 141 are A1. Understand and apply theories and methods of the science technology, engineering and mathematical (STEM) disciplines B3. Apply the appropriate mathematical, statistical or computational strategies to problem solving. MTH 141 Learning Outcomes. At the end of the course the student should be able to: 1. Limits and continuity. Select suitable techniques to/and perform analysis and computation of limits by analytic, graphical and numerical methods, and use limits to investigate properties of functions such as continuity and existence of asymptotes. Investigate continuity properties of functions. 2. Derivatives. Select suitable techniques to/and perform analysis and computation of derivative at a point using limits, numerical, and graphical methods. State the definition of derivative as a limit of a difference quotient, and use it to establish its value or non-existence. Perform analysis of differentiability of a function at a point or a set of points, using limits, numerical, or graphical methods. 3. Computing derivatives algebraically. Select suitable formulas and theorems to/and perform computation of first and higher order derivatives algebraically. Perform computation derivatives of functions defined implicitly. Using Derivatives. Perform analysis and computation using differentiation to/and investigate velocity, acceleration, related rates, monotonicity, optimization problems, linear approximation, limits (L Hopital s rule), and functions defined parametrically. Apply theorems about continuous and differentiable functions (such as the Extreme Value Theorem, the Mean Value Theorem). 5. Integration. Select appropriate technique to perform analysis and computation using Left and Right Riemann sums to approximate integrals. Select suitable formulas and theorems to/and calculate anti-derivatives, and verify answers by differentiation. State the First and Second Fundamental Theorem of Calculus and use it to compute integrals of simple functions, and apply them to total change. Use integrals to compute area of planar regions bounded by simple functions. 6. Modeling, Approximation, Technology. Select calculus methods and use technology to analyze mathematical models and determine their applicability. Use technology to analyze accuracy of approximations, perform numerical and symbolic calculations, and produce graphical representations of functions to investigate their properties. 7. Written Mathematical Communication. Communicate effectively in written form mathematical ideas and solutions, by stating in a complete, clear, concise, and organized manner steps, calculations, solution strategy, conclusions, and when appropriate, interpreting results in practical or applied terms. 2/5

5 MTH 141 Spring Calendar The following calendar gives a timetable for the course. Your class may be slightly behind or ahead at any given time. Some of the problems may be done in class, others as homework. You should work out all the problems given below. Notation like "3-9" means that all problems from 3 to 9 are to be done. Starred problems require technology. Textbook: Calculus: Single Variable, by Hughes-Hallet et al, 6th ed., Wiley. Week Dates Sections/Events/Exams Problems (*) = requires technology Jan 23 First Day of Class Tuesday. Jan 26 (1.1) Functions and Change (1.1) 1,6,9,12,16*,17,21,26,37,40,43,44*,51,55 1 (1.2) Exponential Functions (1.2) 5-14,22*,23,30*,35*,37,38 Jan 27 (1.3) New Functions From Old (1.3) 1,2,3,8,11,13,15,23,24,28-31,36,37,,55 Jan 30 (1.4) Logarithmic Functions (1.4) 3,7-13,19,20,25,29,30,32*,33*,40*,50* 2 (1.5) Trigonometric Functions (1.5) 14-19,22-23,27,30,33,39,41,43,44,51 Feb 3 (1.6) Powers, Polynomials, and Rational Fns. (1.6) 3-10,19-22,36-38,45*,46* Feb 6 (1.7) Introduction to Continuity (1.7) 2-7,19-21,24-25,27,32,37 3 (1.8) Limits (1.8) 1-3,7-9,12-15,19*,23*,25*,29,31,54-62,64-67 Feb 10 (2.1) How do we measure speed? (2.1) 1,3-5,8,9*,14-17,21,23,24*,25-28 Feb 13 (2.2) The Derivative at a Point (2.2) 1,4,10-13,17*,26*,35-38, (2.3) The Derivative Function (2.3) 1,3,7,9,11,13,15,16,19,21,28,29,31,33,43 Feb 17 (2.4) Interpretations of the Derivative (2.4) 1-4,6,9,11,12,18,21 Feb 20 Presidents Day - no classes Feb 20 Exam 1 Tues. Feb 21, 6:30-8:00 p.m. CBLS (2.5) The Second Derivative (2.5) 2-4,8-13,16,18-23,28-31 (2.6) Differentiability (2.6) 1-4,6*,9,12,16 Feb 24 (3.1) Powers and Polynomials (3.1) 6-47odd, ,60,63,70,71 Feb 27 (3.2) The Exponential Function (3.2) 1-25odd,40,41 6 (3.3) The Product and Quotient Rules (3.3) 3-29odd,31,32,39-42,45,52,53 Mar 3 (3.4) The Chain Rule (3.4) 1-55 odd, 57,58,61,62,67,76ab,77 Mar 6 (3.5) The Trigonometric Functions (3.5) 10,11,18,21,27-30,38,42,62 7 (3.6) The Chain Rule and Inverse Functions (3.6) 1-8,21-28,43,57-59,63,65 Mar 10 (3.7) Implicit Functions (3.7) 1-20odd,26-30,31-33,37 Mar 13 8 Spring Break No Classes Mar 17 Mar 20 Exam 2 Tues. Mar 21, 6:30-8:00p.m. CBLS100 (3.8) Hyperbolic Functions (3.8) 1-11,30 Mar 24 (3.9) Linear Approximation and the Derivative (3.9) 1-7,10,11*,13*,14,20-22,30,31,36,38,39 Mar 27 (3.10) Theorems about Differentiable Functions (3.10) 10,11, (4.1) Using First and Second Derivatives (4.1) 1,4-14,16-19,28-29,33,38-40 Mar 31 (4.2) Optimization (4.2) 1-25odd,27,28,29*,36 Apr 3 (4.3) Optimization and Modeling (4.3) 1-9 odd, 17, 20-21, (4.6) Rates and Related Rates (4.6) 1,2,5,7,11,12,16-19,25-29,33,44 Apr 7 Apr 10 (4.7) L'Hopital's Rule, Growth, and Dominance (4.7) 1-8, 16-18, odd, 48,49 11 (5.1) How Do We Measure Distance Traveled? (5.1) 1-4, 6-12,13,15,17-18,24-25,27 Apr 14 (5.2) The Definite Integral (5.2) 3-4,11-17,19, 22*-28*, 31,32 Apr 17 (5.3) The Fundamental Thm. & Interpretations (5.3) 3-7,9-12,21,31,42 12 (5.4) Theorems About Definite Integrals (5.4) 2-12,13*-17*,21,24,27-30 Apr 21 (6.1) Antiderivatives Graphically and Numerically (6.1) 2-9,13-14,17,19,23,25 Apr 24 Exam 3 Tues. Apr 25, 6:30-8:00p.m. CBLS (6.2) Constructing Antiderivatives Analytically (6.2) 1-60,65-67,70-71 Apr 28 (6.4) The 2 nd Fundamental Theorem of Calculus (6.4) 4-5,11-14,35-38 May 1 Monday May 1st Last day of Class 14 01/19/2017 5/5

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