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1 NEW YORK CITY COLLEGE OF TECHNOLOGY The City University of New York DEPARTMENT: Mathematics COURSE: MAT 2675 TITLE: DESCRIPTION: TEXT: Calculus III A continuation of MAT Topics include polar and parametric equations, vectors, solid analytic geometry, partial derivatives, multiple integrals, vector fields, line integrals and Green s Theorem. Calculus Multivariable Brian E. Blank and Steven G. Krantz, 2 nd edition, Wiley, 2011 CREDITS: 4 PREREQUISITE: MAT 1575 Prepared by Professors Laura Ghezzi, Neil Katz, Thomas Tradler, and Lin Zhou (Spring 2013) A. Testing Guidelines: The following exams should be scheduled: 1. A one-hour exam at the end of the First Quarter. 2. A one session exam at the end of the Second Quarter. 3. A one-hour exam at the end of the Third Quarter. 4. A one session Final Examination. B. A graphing calculator is required.

2 Course Intended Learning Outcomes/Assessment Methods Learning Outcomes Assessment Methods 1. Students will be able to solve problems involving vectors in two-dimensional and three-dimensional space including finding the equation to a line or to a plane. 2. Students will be able to find the equation of a tangent to a parametric curve at a point and to find the arc length of a parametric curve. 3. Students will be able to find partial derivatives and use them to find tangent planes to surfaces and to solve maximum and minimum problems. 4. Students will be able to evaluate multiple integrals and line integrals in two and three dimensional space, including finding areas and volumes. General Education Learning Outcomes/Assessment Methods Learning Outcomes 1. Understand and employ both quantitative and qualitative analysis to solve problems. Assessment Methods 2. Employ scientific reasoning and logical thinking. 3. Communicate effectively using written and oral means. 4. Use creativity to solve problems.

3 New York City College of Technology Policy on Academic Integrity Students and all others who work with information, ideas, texts, images, music, inventions, and other intellectual property owe their audience and sources accuracy and honesty in using, crediting, and citing sources. As a community of intellectual and professional workers, the College recognizes its responsibility for providing instruction in information literacy and academic integrity, offering models of good practice, and responding vigilantly and appropriately to infractions of academic integrity. Accordingly, academic dishonesty is prohibited in The City University of New York and at New York City College of Technology and is punishable by penalties, including failing grades, suspension, and expulsion. The complete text of the College policy on Academic Integrity may be found in the catalog.

4 MAT 2675 Calculus III Text: Calculus Multivariable, Brian E. Blank and Steven G. Krantz, Wiley, 2 nd edition, 2011 Session Section & Topic Homework Vectors in the Plane 9.2 Vectors in Three-dimensional Space 9.3 The Dot Product and Applications (P ) 9.4 The Cross Product (P ) P. 730: 1-23 odd, odd (61 optional) P. 739: 1-7 odd, odd, odd P. 751: 1-15 odd, 29-32, P. 764: 1-13 odd, 47-50, 55-57, Lines and Planes in Space P. 780: 1, 3, 9-19 odd, 25, 27, 33, 35, 41, 43, odd, 77, Vector-Valued Functions -- Limits, Derivatives and Continuity 10.2 Velocity (P ) 10.3 Tangent Vectors and Arc Length (P ) P. 802: 1-3, 5, 6, 11-14, 15-20, odd P. 812: odd P. 822: 1-21 odd, 39, Functions of Several Variables P. 872: 1, 9, 10, 29, 33, 35 7 First Examination Limits and Continuity P. 889: 1, 2, 3, 5, 7, 11, 13, 15, 18, 19, 21, Partial Derivatives P. 897: 1-13 odd, 14, 15, 31, 45, Differentiability and the Chain Rule P. 911: 1-13 odd, 21, Gradients and Directional Derivatives P. 920: 1, 2, 3, 7, 9, 11, 15, 17, 21, 23, 29, 31, 33, 37, 39, Tangent Planes P. 931: 1, 2, 3, 5, 7, 13, 17, 19, 27, 29, Maximum-Minimum Problems P. 944: 1, 3, 4, 5, 7, 9, 11, 17, 19 (22, 23 and 25 optional) Lagrange Multipliers P. 954: 1-15 odd, (22 and 24 optional) 15 Midterm Examination Double Integrals Over Rectangular Regions 12.2 Integration Over More General Regions P. 974: 5-15 odd, 19, 27 P. 982: 1-9 odd, odd

5 Calculation of Volumes of Solids P. 989: 1-5 odd, 9, odd, 25, Polar Coordinates Integrating in Polar Coordinates P. 998: 1, 5, 9-13 odd, odd, odd, 41, (23-29 odd optional) P. 1012: 1, 3, 7-15 odd, 19, 21, odd, (39-43 odd optional) Triple Integrals P. 1019: 1-15 odd, odd Vector Fields P. 1059: 1, 3, 4, 13, 15-17, odd, (9 optional) 23 Third Examination Line Integrals P. 1070: 1-13 odd, odd Conservative Vector Fields and Path Independence Divergence, Gradient, and Curl P. 1084: 1, 3, 5, 9, 11, 13, 19, 21, 23, 25, 29 P. 1093: 1, 3, 7, 11, 15, 17, 25, 27, 31, 33, 37, 39, Green's Theorem P. 1103: 1, 3, 7, 9, odd Surface Integrals P. 1114: 1, 2, 3, 7, 9, 13, 15, odd 29 Review 30 Final Examination

6 MAT 2675 Calculus III Text: Calculus Multivariable, Brian E. Blank and Steven G. Krantz, Wiley, 2 nd edition, 2011 Section and Topic Homework 9.1 Vectors in the Plane P. 730: 1-23 odd, odd (61 optional) 9.2 Vectors in Three-dimensional Space P. 739: 1-7 odd, odd, odd 9.3 The Dot Product and Applications (P ) P. 751: 1-15 odd, 29-32, The Cross Product (P ) P. 764: 1-13 odd, 47-50, 55-57, Lines and Planes in Space P. 780: 1, 3, 9-19 odd, 25, 27, 33, 35, 41, 43, odd, 77, Vector-Valued Functions -- Limits, Derivatives and Continuity P. 802: 1-3, 5, 6, 11-14, 15-20, odd 10.2 Velocity and Acceleration (P ) P. 812: odd 10.3 Tangent Vectors and Arc Length (P ) P. 822: 1-21 odd, 39, Functions of Several Variables P. 872: 1, 9, 10, 29, 33, Limits and Continuity P. 889: 1, 2, 3, 5, 7, 11, 13, 15, 18, 19, 21, Partial Derivatives P. 897: 1-13 odd, 14, 15, 31, 45, Differentiability and the Chain Rule P. 911: 1-13 odd, 21, Gradients and Directional Derivatives P. 920: 1, 2, 3, 7, 9, 11, 15, 17, 21, 23, 29, 31, 33, 37, 39, Tangent Planes P. 931: 1, 2, 3, 5, 7, 13, 17, 19, 27, 29, Maximum-Minimum Problems P. 944: 1, 3, 4, 5, 7, 9, 11, 17, 19 (22, 23 and 25 optional) 11.9 Lagrange Multipliers P. 954: 1-15 odd, (22 and 24 optional) 12.1 Double Integrals Over Rectangular Regions P. 974: 5-15 odd, 19, Integration Over More General Regions P. 982: 1-9 odd, odd 12.3 Calculation of Volumes of Solids P. 989: 1-5 odd, 9, odd, 25, Polar Coordinates P. 998: 1, 5, 9-13 odd, odd, odd, 41, (23-29 odd optional) 12.5 Integrating in Polar Coordinates P. 1012: 1, 3, 7-15 odd, 19, 21, odd, (39-43 odd

7 optional) 12.6 Triple Integrals P. 1019: 1-15 odd, odd 13.1 Vector Fields P. 1059: 1, 3, 4, 13, 15-17, odd, (9 optional) 13.2 Line Integrals P. 1070: 1-13 odd, odd 13.3 Conservative Vector Fields and Path Independence P. 1084: 1, 3, 5, 9, 11, 13, 19, 21, 23, 25, Divergence, Gradient, and Curl P. 1093: 1, 3, 7, 11, 15, 17, 25, 27, 31, 33, 37, 39, Green's Theorem P. 1103: 1, 3, 7, 9, odd 13.6 Surface Integrals P. 1114: 1, 2, 3, 7, 9, 13, 15, odd

SOUTHWEST COLLEGE Department of Mathematics

SOUTHWEST COLLEGE Department of Mathematics COURSE SYLLABUS MATH 2415: CALCULUS III (DISTANCE EDUCATION) SPRING 2015 / SS TERM / CRN 48306 / FEBRUARY 14 MAY 17/ INSTRUCTOR: Dr. Jaime L. Hernández CONTACT