## Exams

Test 3: November 15, 2018.

The test will assess conceptual understanding and applications of the following topics: Separable ODEs, qualitative description of solutions to autonomous ODEs, Taylor Polynomials and approximations. Computational fluency with derivatives is also expected, as well as familiarity with basic concepts of ODEs and some topics covered earlier in the term (such as linearization).

Here is a list of suggested practice problems from various textbooks. Links to textbooks are available on the Resources page.

• Taylor Polynomials
• CLP 1: any problem in section 3.4.2, 3.4.3 (ignore Q7, 8, 11), 3.4.4 (ignore 2, 5), 3.4.5 (ignore 8, 9, 10, 11), 3.4.8, 3.4.9.
• APEX Calculus II: any problem in section 8.7 (ignore Q35, 36, 37).
• Differential Equations:
• Separable ODES: from CLP 2 section 2.4: 4, 10, 12, 13, 14, 15, 16, 17, 18, 20, 23, 25, 26b, 28, 32.
• Qualitative behaviour of solutions of autonomous ODES: from Active Calculus Textbook, Chapter 7. Ignore any questions asking for direction fields and stability of equilibrium solutions.
• section 7.1.5: Exercise 4, 6
• section 7.1.6: Activity 7.2.2
• section 7.2.2: Activity 7.2.3
• section 7.2.4: Exercise 5, 6, 7, 8
• section 7.3.1: Activity 7.3.2 (ignore c), 7.3.3 (ignore a).
• section 7.3.4 Exercise 1, 2, 3, 4.
• section 7.4.2: Activity 7.4.2, 7.4.3, 7.4.4.
• Section 7.4.3: Exercise 1, 2, 3, 4, 5, 6, 7, 8, 9
• Section 7.5.3: Activity 7.5.3
• Section 7.5.3: Exercise 3, 4, 7, 8.
• Section 7.6.1: Activity 7.6.2
• Section 7.6.2: Activity 7.6.3
• Section 7.6.4: Exercise 2, 3, 5, 7.

Test 2: October 30, 2018. Test solutions

The test will assess conceptual understanding and applications of the main topics listed below. Computational fluency is also expected.

Main Topics: Implicit differentiation, Related Rates problems, Growth Models, the basics concepts of Differential Equations. Also covered: the basics concepts about Derivatives and Differentiation Rules, Tangent lines and Linear Approximation.

This is a list of suggested practice problems from the Problem Book.

This is a list of suggested practice problems from the Problem Book.

• 2.2: 4, 5, 6, 7, 10, 11, 16, 19, 21, 26, 27.
• 2.3: 1, 3, 6, 7.
• 2.4: 11, 12, 14, 15, 17.
• 2.6: 12, 15, 16, 17, 19, 20.
• 2.7: 13, 14.
• 2.8: 14, 15, 17, 18, 20, 24, 25, 26
• 2.9: 1, 8, 10, 26, 27, 28, 35
• 2.10: 3, 11, 12, 13, 16, 17, 18, 31.
• 2.11: 2, 4, 6, 8, 11, 12, 14, 15.
• 2.12: 4, 9, 18, 23, 28.
• 2.14: 4, 8, 12, 16, 18
• 3.1: 13, 17.
• 3.2: 2, 4, 8, 9, 10, 13, 17, 20, 22
• 3.3.1: 4, 6, 7, 8, 9, 10
• 3.3.3: 2, 5, 6.
• 3.4.2: 1, 2, 4, 6, 7, 9.
• 4.1: 2, 5, 7, 8, 13, 14, 15.

This is a list of suggested practice problems on Differential Equations from the Active Calculus Book.

• section 7.1.2: Activity 7.1.2a, b, d, e
• section 7.1.3: Activity 7.1.4, Exercise 1, 3, 6
 Final Exam: December 14th 2018 Topics: Limits, Continuity and the Intermediate Value Theorem, the Derivative (definition and differentiation rules), Implicit differentiation, Linear approximation and Taylor polynomials, Rates problems, Tangent line problems, Related rates problems, Exponential growth/decay models, Differential Equations, the Mean Value Theorem, Shape of a curve and Curve Sketching, Optimization. Learning Goals: This is a complete list of concepts and techniques we discussed since the start of term. Not all of the skills and concepts in this list will be tested on the exam. Note that compared to past years, this year we did not cover how to compute Taylor polynomials of composite functions. 2016 December Exam. There is a typo in Q11a: the given Taylor polynomial is for ln(1+x) at x=0 and the question should ask for the 100-th derivative of ln(1+x) at x=0. 2017 December Exam