# This is one of two independent courses which follow

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This is one of two independent courses which follow “Measurement and Geometry for Teachers” (Math 1136) to provide necessary content for middle grade teachers. This course focuses on functions and calculus, including modern and historical perspectives. Prerequisite: A grade of C- or above in “Measurement and Geometry for Teachers” (Math 1136). A grade of C- or above in Math 1149 or 1150, or credit for 150, or math placement level L. Text: Calculus, by Frank Morgan, CreateSpace Independent Publishing Platform, ISBN 9781478356882 Purpose: This course serves to introduce students to the key ideas of calculus and to important historical developments in the subject. A thorough introduction to functions as mappings is given, and the trigonometric functions are used throughout the course as a key example of functions not given by algebraic expressions. The essential concepts of limit, derivative, integral, and the fundamental theorem are emphasized, together with core applications. An introduction to Taylor series, especially the Taylor expansions for sine and cosine, completes the class. Topics List: 1. Functions 2. Elementary approach to how functions change 3. Defining rate of change 4. Concept of limit 5. Derivatives 6. Interpretations of first and second derivatives 7. Sine, cosine and logarithm functions 8. Product rule and chain rule 9. Applications of derivatives 10. Antiderivatives 11. Riemann sums 12. Fundamental theorem of calculus 13. Applications of integration 14. Taylor approximations, infinite sequences 15. Series
Page 1 2019-2020 Math 2153 Mathematics 2153 Calculus III Autumn, Spring, Summer 4 credits Catalog Description: Multivariable differential and integral calculus. Prerequisites: C- or better in 1152, 1172, 1534, 1544, 1181H, or 4181H; or credit for 153.xx, 154, 162.xx, or 162.01H. Exclusions : Not open to students with credit for any higher numbered math class, or for any quarter math class numbered 254 or higher. Text: Calculus for Scientists and Engineers: Early Transcendentals , 2 nd OSU custom edition, by Briggs, Cochran, Gillett, published by Pearson, ISBN: 9781256776468 Topics : CHAPTER 12. Vectors and Vector-Valued Functions Section 1. Vectors in the Plane Section 2. Vectors in Three Dimensions Section 3. Dot Products Section 4. Cross Products Section 5. Lines and Curves in Space Section 6. Calculus of Vector-Valued Functions Section 7. Motion in Space Section 8. Length of Curves Section 9. Curvature and Normal Vectors CHAPTER 13. Functions of Several Variables Section 1. Planes and Surfaces, and brief conic section review via pages 761 to 766 of Section 11.4 Section 2. Graphs and Level Curves Section 3. Limits and Continuity Section 4. Partial Derivatives Section 5. The Chain Rule Section 6. Directional Derivatives and the Gradient Section 7. Tangent Planes and Linear Approximation Section 8. Maximum/Minimum Problems Section 9. Lagrange Multipliers
Page 2 2019-2020 Math 2153 Mathematics 2153 Calculus III Autumn, Spring, Summer 4 credits CHAPTER 14. Multiple Integration Section 1. Double Integrals over Rectangular Regions Section 2. Double Integrals over General Regions Section 3. Double Integrals in Polar Coordinates Section 4. Triple Integrals
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