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Math S-1ab
Syllabus
Textbook
Q & A
Harvard Summer School
Course Description
Academic Policies
Harvard Math Department
Matthew Leingang
Robin Gottlieb
Dawei Chen
Faculty Resources
GoodQuestions
Summer School
Instructor's Toolkit
Homework
Homework will be assigned each class day and due the next class day. It is extremely important that you keep up and complete your homework on time. Not only does it count for 25% of your course grade, homework is the best place to actually learn what's covered in class.
Reading Assignments: the night before each class you should read the section(s) covered for that class. Come to class prepared to ask and answer questions!
Solutions: if the text of a problem set is highlighted, solutions are available though the link.
| Date | Sections | Problems | Due |
|---|---|---|---|
| 6/29 (T) | 2.1: The Tangent and Velocity Problems | 2, 5, 8, 9 | 6/30 |
| 2.2: The Limit of a Function | 7, 8, 10, 22 | ||
| 6/30 (W) | 2.3: Calculating Limits Using the Limit Laws | 1, 2, 5, 8, 14, 18, 30, 32 | 7/1 |
| 2.4: Continuity | 2, 4, 6, 8, 14, 20, 30, 32 | ||
| 7/1 (Θ) | 2.5: Limits Involving Inifinity | 1, 4, 6, 14, 18, 21, 23, 35 | 7/2 |
| 2.7: Derivatives | 1, 2, 3, 13, 14, 18, 19, 22 | ||
| 7/2 (F) | 2.8: The Derivative as a Function | 2, 3, 4, 9, 10, 30, 31, 36 | 7/6 |
| 2.9: Linear Approximations | 2, 4, 6, 7, 8, 10, 12, 13 | ||
| 7/5 (M) | Holiday: No Class | ||
| 7/6 (T) | 3.1: Derivatives of Polynomials and Exponential Functions | 1, 2, 9, 19, 22, 24, 32, 36 | 7/7 |
| 3.2: The Product and Quotient Rules | 2, 4, 8, 10, 20, 22, 28, 34 | ||
| 7/7 (W) | 3.4: Derivatives of Trigonometric Functions | 4, 7, 10, 14, 18, 30, 37, 40 | 7/8 |
| 3.5: The Chain Rule | 3, 6, 17, 27, 31, 38, 42, 44 | ||
| 7/8 (Θ) | 3.6: Implicit Differentiation | 1, 4, 13, 18, 21, 24, 39, 43 | 7/9 |
| 3.7: Derivatives of Logarithmic Functions | 1, 2, 5, 6, 10, 20, 35, 36 | ||
| 7/9 (F) | 3.8: Linear Approximations and Differentials | NONE | 7/12 |
| 3.3: Rates of Change in the Natural and Social Sciences | 1, 2, 4, 14, 20, 22, 25, 29 | ||
| 7/12 (M) | 4.1: Related Rates | 2, 5, 6, 8, 12, 14, 25 | 7/13 |
| Midterm I | |||
| 7/13 (T) | 4.2: Maximum and Minimum Values | 1, 2, 3, 6, 7, 9, 12, 39 | 7/14 |
| 4.3: Derivatives and Shapes of Curves | 2, 3, 4, 6, 7, 12, 18, 29 | ||
| 7/14 (W) | 4.5: Indeterminate Forms and L'Hôpital's Rule | 1, 4, 9, 12, 27, 33, 54, 58 | 7/15 |
| 4.7: Applications to Economics | 1, 3, 4, 5, 10, 15, 16, 18 | ||
| 7/15 (Θ) | 4.6: Optimization Problems | 4, 7, 8, 10, 19, 22, 23, 32 | 7/16 |
| 7/16 (F) | 4.8: Newton's Method | 1, 3, 4, 6, 9, 22 | 7/19 |
| 4.9: Antiderivatives | 6, 8, 10, 24, 27, 30, 33, 34 | ||
| 7/19 (M) | 5.1: Areas and Distances | 1, 2, 3, 7, 11, 12, 13, 18 | 7/20 |
| 5.2: The Definite Integral | 1, 6, 20, 23, 30, 32, 40, 41 | ||
| 7/20 (T) | 5.3: Evaluating Definite Integrals | 1, 2, 4, 12, 18, 28, 49, 57 | 7/21 |
| 7/21 (W) | 5.4: The Fundamental Theorem of Calculus | 3, 4, 9, 12, 15, 19, 22, 24 | 7/22 |
| 7/22 (Θ) | 5.5: The Substitution Rule | 4, 5, 16, 18, 28, 45, 51, 61 | 7/23 |
| 7/23 (F) | Review | ||
| Midterm II | |||
| 7/26 (M) | 5.6: Integration by Parts | 4, 6, 9, 14, 18, 22, 28 | 7/27 |
| 5.7: Partial Fractions + Techniques | 16, 18, 24, 27, 29 | ||
| Int. PS #2, 3, 4 | |||
| 7/27 (T) | 5.9: Approximate Integration | 1, 2, 23 | 7/28 |
| 5.10:Improper Integrals | 2, 12, 14, 20, 24, 29, 51 | ||
| Int. PS #5, 26 | |||
| 7/28 (W) | 6.1: Areas | 2, 25 | 7/29 |
| Int. PS #8, 11, 12 | |||
| 6.2 : Volumes | 21, 23, 28, 37, 42 | ||
| 7/29 (Θ) | G:27.1: Slicing | Int. PS # 13, 14, 15, 16, 17, 19, 20, 21 | 7/30 |
| 6.3: Arc Length | 4 | ||
| 7/30 (F) | 6.4: Average Value | 2, 11 | 8/2 |
| 6.5: Work | 4, 7, 8, 10, 12, 13, 14 | ||
| Int. PS #24 | |||
| 8/2 (M) | 8.1: Sequences | 39 | 8/3 |
| 8.2: Series | 1, 2, 12, 16, 18, 20, 48, 51 | ||
| Series PS # 1, 2, 3, 4, 5 | |||
| 8/3 (T) | 8.3: Integral and Comparison Test | 1, 2, 5, 15, 16, 18, 19, 20, 22 | 8/4 |
| 8.4: Alternating Series Test | 12, 13, 19 | ||
| Series PS #9 a,b,c, 15, 19 | |||
| 8/4 (W) | G:30.1 Approximating a Function by a Polynomial | G:30.1 #1, 2, 9, 11, 12, 13 | 8/5 |
| Series PS #10, 11, 12, 13, 14 | |||
| 8.7 : Taylor Series | (ignore R_n(x) for now) 7, 13, 18, 20, 22 | ||
| 8/5 (Θ) | 8.4: Ratio Test | 2, 20, 22, 31, 33 | 8/6 |
| 8.5: Power Series | 4 | ||
| 8/6 (F) | Midterm Exam | 8/9 | |
| 8.5: Power Series | 12, 14, 16, 20 | ||
| 8/9 (M) | 8.6: Representations of Functions as Series | 9, 11 | 8/10 | ^M
| Series PS # 20, 21, 22, 24, 25 | 8.7:Taylor Series (and 8.8) | 8.7: 11(no R_n), 29, 34, 36; 8.8: 1, 9 |
|
| 8/10 (T) | 7.1: Modeling with Differential Equations | 4, 5, 7, 11 | 8/11 |
| 7.2:Direction Fields (Euler's briefly) | 3, 4, 5, 6 | ||
| Diff EQ PS #1, 2, 3, 4, 5, 6 | |||
| 8/11 (W) | 7.3: Separation of Variables | 4, 10, 34, 36 | 8/12 |
| Diff EQ PS #7, 8, 9, 10 (b refers to 10ai) 11, 12 | |||
| 7.4 : Exponential Growth and Decay | 19 bcd | ||
| 8/12 (Θ) | G: 31.3: Qualitative Solns to Autonomous Diff Eqns 7.5: Logistic Equation |
G: 31.3 # 1, 2, 3, 6 | 8/13 |
| 7.6 Predator-Prey Systems | 1, 2, and Chptr 7 Rev. #20, 21 (where in 20 the trajectories are closed curves) | ||
| Diff EQ PS #13, 14 | |||
| 8/13 (F) | Systems of Differential Equations | ||
| Possibly First Order Linear Differential Equations | |||
| &bsp; | |||
