{"id":35071,"date":"2023-09-03T18:26:17","date_gmt":"2023-09-03T10:26:17","guid":{"rendered":"https:\/\/www.fst.um.edu.mo\/personal\/?page_id=35071"},"modified":"2023-09-03T18:26:35","modified_gmt":"2023-09-03T10:26:35","slug":"math1003","status":"publish","type":"page","link":"https:\/\/www.fst.um.edu.mo\/personal\/liluo\/math1003\/","title":{"rendered":"MATH1003"},"content":{"rendered":"

 <\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Coordinating Unit:<\/td>\nDepartment of Mathematics, Faculty of Science and Technology<\/td>\n<\/tr>\n
Supporting Unit(s):<\/td>\nNil<\/td>\n<\/tr>\n
Course Code:<\/td>\nMATH1003<\/td>\nYear of Study:<\/td>\n1<\/td>\n<\/tr>\n
Course Title:<\/td>\nIntermediate Calculus<\/td>\n<\/tr>\n
Compulsory\/Elective:<\/td>\nCompulsory<\/td>\n<\/tr>\n
Course Prerequisites:<\/td>\nGEST1004 Quantitative Reasoning for Science and Technology<\/td>\n<\/tr>\n
Prerequisite Knowledge:<\/td>\nNil<\/td>\n<\/tr>\n
Duration:<\/td>\nOne semester<\/td>\nCredit Units:<\/td>\n3<\/td>\n<\/tr>\n
Class\/Laboratory Schedule:<\/td>\nThree hours of lecture and one hours of tutorial per week.<\/td>\n<\/tr>\n
Laboratory\/Software Usage:<\/td>\nNil<\/td>\n<\/tr>\n
Course Description:<\/td>\nThis course is a continuation of the course Quantitative Reasoning for Science and Technology. The topics include methods of integration, parametric curves, sequence and series, vectors and curves in space. The two courses together aim at providing students with a solid foundation of one variable calculus.<\/td>\n<\/tr>\n
Course Objectives:<\/td>\n1.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 To introduce more methods of integration, and parametric curves<\/p>\n

2.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 To introduce sequence and series<\/p>\n

3.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 To introduce vectors and curves in space<\/td>\n<\/tr>\n

Learning Outcomes (LOs):<\/td>\nUpon completion of this course, students are expected to:<\/p>\n

1.\u00a0\u00a0\u00a0\u00a0\u00a0 Be able to find integrals using various methods.<\/p>\n

2.\u00a0\u00a0\u00a0\u00a0\u00a0 Be able to do computations with parametric curves.<\/p>\n

3.\u00a0\u00a0\u00a0\u00a0\u00a0 Be able to identify and use infinite series.<\/p>\n

4.\u00a0\u00a0\u00a0\u00a0\u00a0 Be able to solve problems with vectors and curves in space.<\/td>\n<\/tr>\n

Texts & References:<\/p>\n

\u00a0<\/em><\/p>\n

(* recommended textbook(s))<\/em><\/td>\n

1.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 *Calculus, Early Transcendentals Version, 7th<\/sup> Ed, C. H. Edwards and D. E. Penney, Prentice Hall.<\/p>\n

2.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Calculus and analytical geometry, 9th<\/sup> Ed. Thomas and Finney, Addison Wesley.<\/td>\n<\/tr>\n

Student Assessment:<\/td>\n\u2022\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Assignments: 15%<\/p>\n

\u2022\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Midterm examination: 25%<\/p>\n

\u2022\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Final examination: 60%<\/td>\n<\/tr>\n

Learning Outcome Assessment:<\/td>\n\u2022 \u00a0\u00a0\u00a0 Assignments, midterm and final examination<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u00a0<\/em><\/p>\n\n\n\n
Course Content: (topic outline)<\/td>\n <\/p>\n\n\n\n\n\n\n\n\n\n\n
Week no.<\/td>\nTopics<\/td>\nAssignment no.<\/td>\nLO no.<\/td>\n<\/tr>\n
1-3<\/td>\nTechniques of integration <\/strong><\/p>\n

Substitution, integration by parts, trigonometric integrals, partial fractions, trigonometric substitution, improper integral<\/td>\n

1 – 3<\/td>\n1<\/td>\n<\/tr>\n
4, 5<\/td>\nPolar coordinate and parametric curves <\/strong><\/p>\n

Area computation in polar coordinates, parametric curves, integral computations with parametric curves<\/td>\n

4, 5<\/td>\n2<\/td>\n<\/tr>\n
6, 7<\/td>\nInfinite sequence <\/strong><\/p>\n

Convergence of sequence, operations of limit of sequences<\/td>\n

6<\/td>\n3<\/td>\n<\/tr>\n
7<\/td>\nMidterm examination<\/strong><\/td>\n<\/td>\n<\/td>\n<\/tr>\n
8-12<\/td>\nInfinite series <\/strong><\/p>\n

Infinite series and convergence, Taylor series and Taylor polynomials, integral test, comparison test, alternating series and absolute convergence, power series\u00a0 <\/strong><\/td>\n

7-10<\/td>\n3<\/td>\n<\/tr>\n
13-15<\/td>\nVectors, curves and surface in space <\/strong><\/p>\n

Vectors in plane and space, cross product, lines and planes, curves and motion in space, curvature and acceleration, cylinder and quadric surfaces, cylindrical and spherical coordinates<\/td>\n

11 – 13<\/td>\n4<\/td>\n<\/tr>\n
TBA<\/td>\nFinal Examination <\/strong><\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

  Coordinating Unit: Department of Mathematics, Faculty of Science and Technology Supporting Unit(s): Nil Course Code: MATH1003 Year of Study: 1 Course Title: Intermediate Calculus Compulsory\/Elective: Compulsory Course Prerequisites: GEST1004 Quantitative Reasoning for Science and Technology Prerequisite Knowledge: Nil Duration: One semester Credit Units: 3 Class\/Laboratory Schedule: Three hours of lecture and one hours of … <\/p>\n

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