Calculus — MATH201–203

Contents: Chapters:  P. Precalculus 1. Limits 2. Derivatives 3. Applied Derivatives 4. Integrals 5. Logs and Exponentials 10. Vectors 12. Multivariable general handouts

Quickies: TI calc.  |  Study tips  |  IQ Web  |  Browser issues

Handouts (for all students)

( indicates a non-TC3 Web site.)

P. Preparation for Calculus

• P.3 – Evaluating Functions with the TI-83/84 (rev. Aug 5, 2007)
• P.3 – Graphing Functions on the TI-83/84 (rev. Aug 5, 2007)
• P.4 – Least Squares Regression on the TI-83/84 (rev. Aug 8, 2007)
• P.4 – Scatter Plot, Correlation, and Regression on the TI-83/84 (rev. Sep 9, 2007) and a version for the TI-89
• P.4 – Getting ŷ from Any x in a Regression on the TI-83/84/89 (rev. Aug 7, 2007)
• other – It’s the Law — the Laws of Exponents
• other – Combining Operations (Distributive Laws)
  Why is it legal to factor 2x+2y as 2(x+y), but not x²+y² as (x+y)²?
• other – 10-Minute Trig
  a fast summary of the key definitions and relations

1. Limits and Their Properties

• 1.2 – Evaluating Functions with the TI-83/84 (rev. Aug 5, 2007), including TABLE and TRACE methods
• 1.2 – Graphing Piecewise Functions on the TI-83/84 (rev. Aug 5, 2007)

2. Differentiation

• 2.1 – lecture review: The Derivative and the Tangent Line (Jun 8, 2005) — lecture notes for section 2.1
• 2.1, 2.2 – Derivatives on the TI-83/84 (rev. Apr 29, 2006)
• 2.2 – A Tangent Line Problem (Jul 9, 2005) — page 114 problem 65
• 2.2–2.4 – lecture review: Derivatives — Key Formulas (Jun 8, 2005)
• 2.6 – Related Rate Problems from Business (Jun 8, 2005)

3. Applications of Differentiation

• 3.3, 3.4 – lecture review: Finding Relative Extrema (Jun 8, 2005)
• 3.6 – lecture review: Sketching Curves (Jun 8, 2005)
• 3.7 – lecture review: Optimization (Jun 8, 2005)
• 3.8 – advanced material: Newton’s Method on the TI-83/84 or TI-89 (rev. Aug 5, 2007)

4. Integration

• 4.1 – lecture review: Antiderivatives and Indefinite Integration (Jul 23, 2003)
• 4.2 – advanced material: Area by Upper and Lower Sums (Jan 12, 2004)
• 4.3, 4.4 – advanced material: Definite Integrals on the TI-83/84 (rev. Jul 20, 2003)
• 4.5 – lecture review: Changing Variables in Integrals (u-Substitution) (Jan 12, 2004)

5. Logarithmic, Exponential, and Other Transcendental Functions

• 5.1 – It’s the Law Too—the Laws of Logarithms reviews the precalculus laws of logarithms
• 5.3 – Drawing Inverse Functions on the TI-83/84 (rev. Aug 5, 2007)
• 5.3 – Unexpected Occurrences of the Number e (PDF) by Harris S. Shultz and Bill Leonard

10. Vectors and the Geometry of Space

• 10.1, 10.2 – Adding Vectors Graphically on the TI-83/84 (rev. Aug 7, 2007)
• 10.3. 10.4 – Multiplying Vectors on the TI-83/84 (rev. Aug 7, 2007)
• 10.4 – Irina Nelson and Johnny Erickson’s Magnetism gives an excellent picture of the right-hand rule for vector cross products

12. Functions of Several Variables

• 12.9 – Least Squares Regression on the TI-83/84 (rev. Aug 8, 2007)
• 12.9 – Scatter Plot, Correlation, and Regression on the TI-83/84 (rev. Sep 9, 2007) and a version for the TI-89
• 12.10 – Michael Trick’s Equality Constraints (Lagrangians) is, I think, a bit clearer than your textbook. There’s a good Geometric Interpretation, and a particularly good Economic Interpretation of the multiplier λ.

General

• Help! (Jan 18) — sources of assistance
• Recommended Books and Web Sites (Jul 9, 2005)
• Show Your Work! (Aug 19, 2005)
• Study Guide for the Exams (Aug 15, 2004)
• Web Supplements to Your Textbook (Jun 8, 2005) — links to the “missing” appendices, large-format graphs, and the articles mentioned in the margins of your textbook
• TI-83/84 Troubleshooting (rev. Aug 5, 2007)
• How to Succeed in Math (Aug 16, 2007) includes Why is Math so Hard?  |  How to Study Math  |  How to Take a Math Test  |  How to Read a Math Book  |  How to Work a Math Problem
• Math Students’ FAQ (Mar 5, 2003)