## Math 105 - Topics Schedule and Learning Goals

The course is divided into three parts. Roughly speaking, we will cover multivariable calculus (Chapter 12) and start on integration (Chapter 5) before the first midterm. We will complete the theory of integration (Chapter 5) and integration techniques (Chapter 7), followed by a week's worth of probability before the second midterm. The rest of the time will be devoted to discussing sequences and series (Chapters 8 and 9).

Here is an approximate week-by-week schedule of course material based on the appropriate sections of the text. The chapter and section numbers are from the third custom edition of the textbook. Follow the links for each week to get a more detailed description of the concepts covered that week, and for the learning objectives that you should use as self-checks.
• Week 1 (Jan 2--4): Functions of several variables (Chapter 12) Learning goals
• Planes and surfaces (12.1)
• Graphs and level curves (12.2)
• Week 2 (Jan 7--11): Functions of several variables (Chapter 12) Learning goals
• Partial derivatives (12.4)
• Maximum/minimum problems (12.8)
• Week 3 (Jan 14--18): Functions of several variables (Chapter 12) Learning goals
• Maximum/minimum problems (12.8)
• Lagrange multipliers (12.9)
• Week 4 (Jan 21-- Jan 25 ): Integration (Chapter 5) Learning goals
• Approximating areas under curves (5.1)
• Definite integrals (5.2)
• Week 5 (Jan 28--Feb 1): Definite integrals (5.2)+Review + Midterm 1
• Week 6 (Feb 4--8): Integration (Chapter 5) and Integration techniques (Chapter 7) Learning goals
• Fundamental theorem of calculus (5.3)
• Substitution rule (5.5)
• Integration by parts (7.1)
• Week 7 (Feb 11--15): Integration techniques (Chapter 7) Learning goals
• Trigonometric integrals (7.2)
• Trigonometric substitutions (7.3)
• Partial fractions (7.4)
• Week 8 (Feb 25--Mar 1): Integration techniques (Chapter 7) Learning goals
• Numerical integration (7.6)
• Improper integrals (7.7)
• Introduction to differential equations (7.8)
• Week 9 (Mar 4--8): Probability ( Probability Appendix) Learning goals
• Random Variables and Probability Basics ( 1.1 and 1.2 in Probability Appendix)
• Continuous random variable ( 2.1, 2.2 and 2.3 in Probability Appendix)
• Expected Value, Variance, and Standard Derivation (2.5 in Probability Appendix)
• Week 10 (Mar 11--15): Review + Midterm 2
• Week 11 (Mar 18--22): Sequences and infinite series (Chapter 8) Learning goals
• Sequences (8.1-8.2)
• Infinite series (8.3)
• The divergence and integral tests (8.4)
• Week 12 (Mar 25--29): Series (Chapter 8) and Power series (Chapter 9) Learning goals
• The ratio, root and comparison tests (8.5).
• Approximating functions with polynomials (9.1)
• Properties of power series (9.2)
• Week 13 (Apr 1--5): Power series (Chapter 9) and review Learning goals
• Taylor series (9.3)
• Working with Taylor series (9.4)