SM121 Syllabus (Calculus I), Fall AY 2020-2021 
                            
       Text: “CALCULUS, Early Transcendentals", Eighth Edition, by James Stewart 
       Course coordinator: Irina Popovici, popovici@usna.edu 
        
                         Overview 
       SM121 is the first course in the three-semester sequence SM121-122-221/223 covering the 
       standard differential and integral calculus methods for students pursuing a bachelor of science. 
       Calculus is the study of how things change; it provides a framework for modeling systems in which 
       there is change, and a way to predict the behavior of such models.  It is a 4-credit course, whose 
       pre-requisite is Pre-calculus.  
        
       There is a long list of USNA courses where you will continue using the computations and analyses 
       taught in calculus (core: physics SP211, SP212, principles of engineering EE301, EE302, principles of 
       propulsion/navigation, weapons/systems EN400/EA400, ES300, ES360/ES420; major-required: 
       Econ 201-202, PoliSci 220, Oceanography SO271, SO335, Aero EA232, Computer Engineering 
       EE221, etc.).  
        
       Given the long-term impact that your calculus skills have in subsequent USNA courses (and in many 
       of Navy’s warfare communities), it is important that you make it a priority to adhere to the 
       guideline of studying 2 hours for each hour in class (approx. 7 hours per week).  
        
                       Learning outcomes 
                            
       Upon successful completion of this course, students will be able to: 
          1. Interpret, analyze, create, and communicate mathematical models involving derivatives. 
          2. Carry out computations involving order of growth, limits and derivatives. 
          3. Describe relations between geometry, formulas, and data. 
          4. Recognize and apply mathematical procedures to solve applied problems, including 
          related rates and optimization. 
          5. Write simple proofs of mathematical results. 
        
       In addition to the listed topics, there is an implied curriculum of verbal and cognitive skills, of 
       abstraction and interpretation, equal in importance to the core topics listed in the table of 
       contents.  
       A key ingredient for success in this course is communication of solutions. In homework you should 
       practice writing the entire argument for your solutions instead of just recording “answers". There 
       will be a number of proofs on tests and the final exam (such as proving the differentiation rules for 
       quadratic functions, the exponential function, the sine function, and product rule).  
        
                         Technology 
         
       All students in this course are expected to have the TI-36X Pro calculator; there may be questions 
       on the common final exam for which it is expected that the student has such a calculator. There 
       may also be exam problems for which no calculator is allowed, and homework problems requiring 
       graphing software (via laptops).  
                All students are required to enroll in WebAssign. The first time you log into WebAssign you must 
                create your account through Blackboard. Some instructors may choose to not grade problems via 
                WebAssign this semester; nonetheless all students should enroll now. WebAssign is more than a 
                homework portal: it provides access to study materials; it will be in place for future semesters.  
                 
                The online teaching environment gives students broader access to resources than an in-person set 
                up. Be extra careful to follow the instructions given to you about what is allowed and what is not 
                when completing and turning in work. Midshipmen are persons of integrity. They do not cheat. 
                 
                                            Help beyond your instructor’s Extra Instruction 
                                                                       
                The Midshipmen Group Study Program (https://intranet.usna.edu/AcCenter/MGSP/ ) provides 
                regularly scheduled, out-of-class, peer-led group study sessions. MGSP sessions for this course are 
                typically available Sunday - Thursday evenings, 2000-2200. No appointment is necessary. 
                 
                The Class of 1963 Center for Academic Excellence (https://intranet.usna.edu/AcCenter/index.php) 
                provides workshops on time management, test preparation, and other learning skills for all 
                midshipmen. For Calculus I, they provide periodic extra review sessions and they provide a one 
                hour, non-credit Supplemental Instruction class (XS121). They also provide professional tutoring, 
                both in evening “walk-in” sessions and in scheduled daytime one-on-one sessions.  
                 
                The Math Department’s website has more resources for the course, including practice midterms 
                and final exams (http://www.usna.edu/MathDept/resources/course-materials.php). Additionally, 
                there are a wealth of free calculus resources (e.g., graphing apps like desmos.com, geogebra.org).  
                 
                                            Assignments (subject to change by instructors) 
                 
                  Day              Section in Stewart                                         Homework 
                  01    Appendix A, B, C: Pre-calculus  review     A15 (B): 12,17,20,24,26,31,32,33, 40, 51, 57; A23 (C): 4, 11, 13, 20 
                  02    continued (gateway quiz administration)                                     
                  03    Appendix D:  Trigonometry Review           A32 (D): 3, 10, 12, 13, 14, 20, 21, 30(sin, cos only), 37, 59, 67 
                  04    1.1 Representing Functions                 p.19: 1, 4, 7, 8, 9, 11, 14, 20, 24, 25, 26, 27, 29, 30, 34,43 
                  05    1.1 Representing Functions II              p.19: 52, 53, 58 63, 64, 66, 69, 70, 72, 73, 75, 78 
                  06    1.2 Mathematical Models                    p.33: 1,3, 4, 12, 15, Handout1.2 
                  07    1.3 New Functions from Old                 p.42: 1, 2be,3abe, 4,5,6 11, 12, 13, 14,15, 17,  
                  08    continued                                  p.42 28, 35ab, 46, 52abf, 53abc,55,57,58 
                  09    1.4 Exponents                              p.53: 1, 2, 4, 7, 8,11, 15, 23,30 
                  10    1.5 Inverse Functions & Logarithms          p.66: 2, 3, 7, 8, 10, 11, 12, 13, 15, 18, 19, 22, 23, 25, 29 
                  11                   continued                   p.67: 26, 35, 36, 38, 39, 40, 49, 50, 51, 53b, 62, 63, 
                  12                     Review                    p.70: 3, 7, 10ace, 15, 17bd, 22, 25 
                  13                     Test 1                                                     
                  14    Tangent and Velocity                       p.82: 1,3 a(ii, iv,vi, viii), b c, 6a(ii, iii, iv)b, 9a (0.7 to1.2 only),b c 
                  15    2.2 Limits / Limit Laws                    p.92: 4, 6, 9, 10, 12, 18, 31, 44 
                  16    2.3 Limit Laws                             p.103: 1, 2, 9, 11, 23, 24, 32, 50 
                  17    2.5 Continuity                             p.124: 4, 9, 18, 19, 20, 37, 39, 45, 47, 53, 55 
                  18    2.6 Limits at Infinity; handout            p.137: 3, 4 ,6, 8, 10, 15, 16, 20, 27, 30, 35, 37, 50, 58 
                  19    2.7 Rates of Change                        p.148: 1, 3, 11, 12, 14, 17, 19, 23, 25, 34, 37, 38 
                  20    continued                                  p.148: 41, 42, 45, 46, 47, 48ab, 53bc, 55, 57 
                  21    2.8 Derivative as a Function               p.160: 1,3,5,9,14a for F'(15),bc,21,24,35ab for 2010,42,53,57b 
                  22    Review and PROOFS (quadratic, 1/x)          
                  23                     Review                                                     
                  24                     Test 2                                                     
                  25    3.1 Deriv. of Polynomials, Powers, Exp.    p.180: 3, 4, 5, 7, 9, 10, 13, 18, 19, 22, 25, 34, 35, 47, 49, 60,65 
                  26    3.2 Product and Quotient Rules             p.188: 4, 5, 8, 12, 18, 23, 27, 32, 44, 46, 47, 50, 58 
                  27     3.3 Derivatives of Trig Functions         p.196: 1, 3, 6, 11, 15, 23, 25, 32, 34 
                  28    continued; PROOFS  (Exp., Sin derivative)  p.196: 36, 51; p.267: 23, 52, 82, 89, 107 
                  29     3.4 Chain Rule                            p.204: 2, 3, 9-15, 23, 36, 60, 62, 66b, 67 
                  30    3.4 Chain Rule II                          p. 205: 70, 83, 85; p.267: 14, 59,73, 93 
                  31    3.5 Implicit Derivatives                   p.214: 2, 4, 5, 10, 14, 25, 26, 30,49, 51, 57 
                  32    continued                                   
                  33    3.6 Derivatives of Natural Log             p.223: 2, 5, 6, 9, 19, 23, 34, 36, 43, 44, 51 
                  34    3.7 Rates of Change                        p.233: 1, 4, 5, 7, 11, 13 
                  35    continued                                  p.233: 18, 22, 26, 37 
                  36    3.9 Related Rates                          p.249: 3, 9, 12-15, 17, 22 
                  37    continued                                  p.267: 57, 60, 90, 92, 98, 100 
                  38     3.10 Linearization                        p.256: 1, 2, 6, 7, 10, 23, 24, 30, 40, 43a, 44a 
                  39    Higher order approx.; Taylor Polynomials  Notes;  p.258: 3-and-4, 5-and-6,  
                  40    Taylor Polynomials                         Notes  
                  41                     Review                                                     
                  42                     Test 3                                                     
                  43    4.1 Min and Max                            p.283: 3, 7, 11, 15, 17, 22, 23, 30, 39, 41, 42, 48, 69, 70 
                  44    4.2 Mean Value Theorem                     p.291: 1, 3, 6, 9, 10, 12, 14, 25; p.284:  57, 61, 63, 75 
                  45    4.3 Derivatives / Shape of Graphs          p.300: 2, 5-8, 10, 12ab, 14ab, 15, 34, 36abcd only graph [0,3] for e 
                  46    continued                                  p.301: 17, 24, 26, 31, 32, 37, 43, 52abce, 78 
                  47    4.4 Indeterminate Forms                    p.311: 1, 5, 6, 8, 14, 
                  48    continued                                  handout (pre-calculus-based limits) 
                  49    4.5 Curve Sketching                        p.321: 3, 9, 15, and graph y=4x-ln(e^(2x)-10) 
                  50    continued                                  p.321: 13,21,42,44 
                  51    4.7 Optimization                           p.336: 2, 6, 9, 12, 15, 35, 50 
                  52    continued                                  p. 336:51, 63, 64, 71, 78 
                  53    4.9 Antiderivatives                        p.355: 1, 5, 7, 9, 10, 12, 14, 18, 20, 28, 35, 40, 55, 62, 71, 73, 76 
                  54    continued                                  p.359: 7(do limits at 0, π/4,and π/2), 16, 17, 30, 34, 69, 74, 77 
                  55                     Review                                                     
                  56                     Test 4                                                     
                  57    Review for the Final                                                        
                  58    SOFs and Review for the Final                                               
                 
                        Detailed course content 
        
       1. Describe functions numerically, algebraically, verbally, and graphically. 
       2. Find domain and range of functions. 
       3. Identify symmetry: even and odd functions. 
       4. Use and interpret the absolute value function. 
       5. Build new functions from old with function arithmetic. 
       6. Transform (by shift, stretch, and reflect) and compose functions. 
       7. Identify the geometry of combining or transforming functions. 
       8. Describe properties of exponential functions. 
       9. Use exponential functions to model growth and decay. 
       10. Describe inverse functions numerically, algebraically, verbally, and graphically. 
       11. Define logarithms and use properties of logarithms. 
       12. Test for one-to-one functions. 
       13. Describe the tangent line as a limit of secant lines. 
       14. Describe average versus instantaneous rates of change. 
       15. Describe the limit numerically, analytically, verbally, and graphically. 
       16. Evaluate limits using limit laws to break down complicated functions. 
       17. Compute two-sided and one-sided limits numerically, algebraically, and graphically. 
       18. Identify when limits don't exist. 
       19. Define continuity algebraically, verbally, and graphically. 
       20. Determine points of continuity. 
       21. Give several types of examples of discontinuity. 
       22. Apply the Intermediate Value Theorem to obtain information about solutions of equations. 
       23. Define and find horizontal and vertical asymptotes. 
       24. Compute limits involving infinity. 
       25. Define the derivative as a limit. 
       26. Employ the definition to evaluate the derivative. 
       27. Find an equation for the tangent line. 
       28. Approximate the derivative given discrete data. 
       29. Verbally describe physical meanings of derivatives (first and second) with units. 
       30. Sketch the graph of the derivative from the graph of the original function. 
       31. Describe the derivative as a function rather than a single slope at a point. 
       32. Use the tangent line to linearly approximate a function. 
       33. Compute Taylor polynomials of functions and use them to obtain higher order approximations. 
       34. Use derivatives to determine monotonicity and concavity of the graph. 
       35. Use first and second derivatives to determine local extrema and points of inflection. 
       36. Sketch the graph of a function (up to vertical shift) from the graph of the derivative. 
       37. Differentiate polynomials, exponentials, trigonometric and logarithmic functions. 
       38. Use the product rule, quotient rule, and chain rule for differentiation. 
       39. Apply the derivative as a rate of change in the natural and social sciences. 
       40. Find derivatives implicitly and by logarithmic differentiation. 
       41. Solve related rates problems. 
       42. Find global extrema. 
       43. Apply the Extreme Value Theorem. 
       44. Apply the Mean Value Theorem. 
       45. Use derivative information to sketch curves. 
       46. Use L'Hospital's rule to find the limit of certain quotients. 
       47. Solve optimization word problems. 
       48. Compute elementary antiderivatives.