{"id":23913,"date":"2022-08-09T15:32:46","date_gmt":"2022-08-09T07:32:46","guid":{"rendered":"https:\/\/www.fst.um.edu.mo\/personal\/?page_id=23913"},"modified":"2022-08-09T16:39:15","modified_gmt":"2022-08-09T08:39:15","slug":"math2000","status":"publish","type":"page","link":"https:\/\/www.fst.um.edu.mo\/personal\/liluo\/math2000\/","title":{"rendered":"MATH2000"},"content":{"rendered":"\t\t
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\u00a0 \u00a0<\/strong><\/strong><\/span><\/p>

MATH2000<\/span><\/h2>

\u00a0 \u00a0Lectures: <\/span>11:30 a.m. to 12:45 p.m. (Monday & Thursday) <\/span>E11-1028<\/strong><\/span><\/p>

\u00a0 \u00a0First 4 weeks of lecture online via ZOOM<\/span><\/p>
Passcode<\/span><\/td>534491<\/span><\/td><\/tr>
Join link<\/span><\/td>

https:\/\/umac.zoom.us\/j\/93687684875?pwd=MWV2K3M5WUt2aldnWlpnRzZDbW5Hdz09<\/a><\/span><\/p><\/td><\/tr><\/tbody><\/table>

\u00a0 \u00a0Tutorial: 4:00 p.m. to 4:50 p.m. (Friday) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 E11-1021<\/strong><\/span><\/p>

\u00a0<\/p>

\u00a0 \u00a0Instructor\u00a0 \u00a0<\/strong><\/span><\/p>

\u00a0 \u00a0Dr. Li Luo<\/span><\/p>

\u00a0 \u00a0Email: liluo@um.edu.mo<\/span><\/p>

\u00a0 \u00a0Office: E11-3048\u00a0 \u00a0 \u00a0Office Time:\u00a011:00 a.m. – 12:00 p.m. (Tuesday & Friday)<\/span><\/p>

\u00a0 \u00a0Office Tel. No.: 8822 4290<\/span><\/p>

\u00a0<\/p>

\u00a0 \u00a0Teaching Assistant\u00a0 \u00a0<\/strong><\/span><\/p>

\u00a0 \u00a0Mr. Tianhao Ma<\/span><\/p>

\u00a0 \u00a0Email: yc17444@um.edu.mo<\/span><\/p>

\u00a0 \u00a0<\/span><\/p>

\u00a0 \u00a0Course Note<\/strong><\/span><\/p>

\u00a0 \u00a0Course note 1 (Differentiation of multivariable)<\/a>\u00a0<\/span><\/p>

\u00a0<\/p>

Coordinating Unit:<\/span><\/p><\/td>

Department of Mathematics, Faculty of Science and Technology<\/span><\/p><\/td><\/tr>

Supporting Unit(s):<\/span><\/p><\/td>

Nil<\/span><\/p><\/td><\/tr>

Course Code:<\/span><\/p><\/td>

MATH 2000<\/span><\/p><\/td>

Year of Study:<\/span><\/p><\/td>

2<\/span><\/p><\/td><\/tr>

Course Title:<\/span><\/p><\/td>

Engineering Mathematics I<\/span><\/p><\/td><\/tr>

Compulsory\/Elective:<\/span><\/p><\/td>

Compulsory<\/span><\/p><\/td><\/tr>

Course Prerequisites:<\/span><\/p><\/td>

GEST 1004 Quantitative Reasoning for Science and Technology<\/span><\/p><\/td><\/tr>

Prerequisite Knowledge:<\/span><\/p><\/td>

Differential and integral calculus for functions of one variable<\/span><\/p><\/td><\/tr>

Duration:<\/span><\/p><\/td>

One semester<\/span><\/p><\/td>

Credit Units:<\/span><\/p><\/td>

3<\/span><\/p><\/td><\/tr>

Class\/Laboratory Schedule:<\/span><\/p><\/td>

3 hours of lecture and 1 hour of tutorial per week.<\/span><\/p><\/td><\/tr>

Laboratory\/Software Usage:<\/span><\/p><\/td>

N\/A<\/span><\/p><\/td><\/tr>

Course Description:<\/span><\/p><\/td>

Functions of two or more variables and their derivatives. Local\/global extrema. Multiple integrals. Vector fields. Line integrals. Surface integrals.<\/span><\/p><\/td><\/tr>

Course Objectives:<\/span><\/p><\/td>

1.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Understand the fundamental theories of multivariable calculus.\u00a0<\/span><\/p>

2.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Be able to formulate and solve problems using partial derivatives.\u00a0<\/span><\/p>

3.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Be able to formulate and solve problems using multiple integrals.\u00a0<\/span><\/p><\/td><\/tr>

Learning Outcomes (LOs):<\/span><\/p><\/td>

Upon completion of this course, students are expected to:<\/span><\/p>

1.\u00a0\u00a0\u00a0\u00a0\u00a0 be able to compute partial derivatives;<\/span><\/p>

2.\u00a0\u00a0\u00a0\u00a0\u00a0 be able to calculate double, triple and line integrals;<\/span><\/p>

3.\u00a0\u00a0\u00a0\u00a0\u00a0 understand basic concepts of the conservative field and potential functions.<\/span><\/p><\/td><\/tr>

Texts & References:<\/span><\/p>

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

1.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Calculus Early Transcendentals, 7th edition, by C. H. Edwards and D. E. Penney, Prentice Hall *<\/span><\/p>

2.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Calculus and analytical geometry, 10th ed. Thomas and Finney, Addison Wesley.<\/span><\/p><\/td><\/tr>

Student Assessment:<\/span><\/p><\/td>

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Homework: 10%;<\/span><\/p>

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Midterm examination: 30%<\/span><\/p>

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Final examination: 60%<\/span><\/p><\/td><\/tr><\/tbody><\/table>

Week no.<\/span><\/p><\/td>

Topics<\/span><\/p><\/td>

Assignment no.<\/span><\/p><\/td>

LO no.<\/span><\/p><\/td><\/tr>

1<\/span><\/p><\/td>

12.1 \u2013 12.3 Functions of Several Variables<\/u><\/strong><\/span><\/p>

Domain and Range of Functions<\/span><\/p>

Graphs and Level Curves<\/span><\/p>

Laws of Limits, Composition and Continuity of Functions<\/span><\/p><\/td>

1<\/span><\/p><\/td>

1<\/span><\/p><\/td><\/tr>

2<\/span><\/p><\/td>

12.4 Partial Differentiation<\/u><\/strong><\/span><\/p>

Tangent Planes and Differentials (include Geometric Meaning)<\/span><\/p><\/td>

2<\/span><\/p><\/td>

1<\/span><\/p><\/td><\/tr>

3<\/span><\/p><\/td>

12.5 Multivariable Optimization Problems<\/u><\/strong><\/span><\/p>

Existence Theorem, Critical Points, Derivative Tests<\/span><\/p><\/td>

3<\/span><\/p><\/td>

1<\/span><\/p><\/td><\/tr>

4<\/span><\/p><\/td>

12.6 \u2013 12.8 Multivariable Optimization Problems<\/u><\/strong><\/span><\/p>

First order approximations, Chain Rules and Directional Derivatives<\/span><\/p><\/td>

4<\/span><\/p><\/td>

1<\/span><\/p><\/td><\/tr>

5<\/span><\/p><\/td>

Test 1 (#12.1 \u2013 12.8)<\/u><\/strong><\/span><\/p>

12.9 \u2013 12.10 Multivariable Optimization Problems<\/u><\/strong><\/span><\/p>

Lagrange Multipliers, Critical Points of Functions of Two Variables<\/span><\/p><\/td>

5<\/span><\/p><\/td>

1<\/span><\/p><\/td><\/tr>

6<\/span><\/p><\/td>

13.1 \u2013 13.2 Double and Iterated Integrals<\/u><\/strong><\/span><\/p>

13.3 Area, Volume and Double Integrals<\/u><\/strong><\/span><\/p>

Cross section and Interchange of order of integration<\/span><\/p><\/td>

\u00a0<\/td>

2<\/span><\/p><\/td><\/tr>

7<\/span><\/p><\/td>

13.4 Polar Coordinates<\/u><\/strong><\/span><\/p>

13.5 Application of Double Integral<\/u><\/strong><\/span><\/p>

13.6 Triple Integral, Cross-Section Method<\/u><\/strong><\/span><\/p><\/td>

6<\/span><\/p><\/td>

2<\/span><\/p><\/td><\/tr>

8<\/span><\/p><\/td>

13.7 Cylindrical Coordinates, Spherical Coordinates and their Jacobian<\/u><\/strong><\/span><\/p>

13.8 Surface Area<\/u><\/strong><\/span><\/p><\/td>

7<\/span><\/p><\/td>

2<\/span><\/p><\/td><\/tr>

9<\/span><\/p><\/td>

13.9 Change of Variables in Multiple Integrals<\/u><\/strong><\/span><\/p>

Test 2 (#12.9 \u2013 13.6)<\/u><\/strong><\/span><\/p><\/td>

8<\/span><\/p><\/td>

2<\/span><\/p><\/td><\/tr>

10<\/span><\/p><\/td>

14.1 Vector Fields<\/u><\/strong><\/span><\/p>

14.2 Line Integral<\/u><\/strong><\/span><\/p><\/td>

9<\/span><\/p><\/td>

2<\/span><\/p><\/td><\/tr>

11<\/span><\/p><\/td>

14.3 Fundamental Theorem of Line Integral, Potential Function and Independence of Path<\/u><\/strong><\/span><\/p>

14.4 Green\u2019s Theorem<\/u><\/strong><\/span><\/p><\/td>

10<\/span><\/p><\/td>

2 & 3<\/span><\/p><\/td><\/tr>

12<\/span><\/p><\/td>

14.5 Surface Integral<\/u><\/strong><\/span><\/p>

14.6 Divergence Theorem<\/u><\/strong><\/span><\/p><\/td>

11<\/span><\/p><\/td>

2 & 3<\/span><\/p><\/td><\/tr>

13<\/span><\/p><\/td>

Test 3 (#13.7 \u2013 14.6)<\/u><\/strong><\/span><\/p><\/td>

\u00a0<\/td>\u00a0<\/td><\/tr>

14<\/span><\/p><\/td>

14.7 Stokes\u2019 Theorem<\/u><\/strong><\/span><\/p><\/td>

12<\/span><\/p><\/td>

2 & 3<\/span><\/p><\/td><\/tr>

15<\/span><\/p><\/td>

Review and Final Examination (TBA)<\/strong><\/span><\/p><\/td>

\u00a0<\/td>\u00a0<\/td><\/tr><\/tbody><\/table><\/td><\/tr><\/tbody><\/table>

\u00a0<\/p>

Grading System:<\/span><\/strong><\/span><\/p>

The credit is earned by the achievement of a grade from \u2018A\u2019 to \u2018D\u2019; \u2018F\u2019 carries zero credit.<\/span><\/p>

Grades are awarded according to the following system:<\/span><\/p>

\u00a0<\/span><\/strong><\/span><\/p><\/td>

Letter Grades<\/span><\/strong><\/span><\/p><\/td>

\u00a0<\/span><\/strong><\/span><\/p><\/td>

Grade Points<\/span><\/strong><\/span><\/p><\/td>

\u00a0<\/span><\/strong><\/span><\/p><\/td>

Percentage<\/span><\/strong><\/span><\/p><\/td><\/tr>

\u00a0<\/span><\/p><\/td>

A<\/span><\/p><\/td>

\u00a0<\/span><\/p><\/td>

4.0\u00a0 (Excellent)<\/span><\/p><\/td>

\u00a0<\/span><\/p><\/td>

93-100<\/span><\/p><\/td><\/tr>

\u00a0<\/span><\/p><\/td>

A-<\/span><\/p><\/td>

\u00a0<\/span><\/p><\/td>

3.7\u00a0 (Very good)<\/span><\/p><\/td>

\u00a0<\/span><\/p><\/td>

88-92<\/span><\/p><\/td><\/tr>

\u00a0<\/span><\/p><\/td>

B+<\/span><\/p><\/td>

\u00a0<\/span><\/p><\/td>

3.3<\/span><\/p><\/td>

\u00a0<\/span><\/p><\/td>

83-87<\/span><\/p><\/td><\/tr>

\u00a0<\/span><\/p><\/td>

B<\/span><\/p><\/td>

\u00a0<\/span><\/p><\/td>

3.0\u00a0 (Good)<\/span><\/p><\/td>

\u00a0<\/span><\/p><\/td>

78-82<\/span><\/p><\/td><\/tr>

\u00a0<\/span><\/p><\/td>

B-<\/span><\/p><\/td>

\u00a0<\/span><\/p><\/td>

2.7<\/span><\/p><\/td>

\u00a0<\/span><\/p><\/td>

73-77<\/span><\/p><\/td><\/tr>

\u00a0<\/span><\/p><\/td>

C+<\/span><\/p><\/td>

\u00a0<\/span><\/p><\/td>

2.3<\/span><\/p><\/td>

\u00a0<\/span><\/p><\/td>

68-72<\/span><\/p><\/td><\/tr>

\u00a0<\/span><\/p><\/td>

C<\/span><\/p><\/td>

\u00a0<\/span><\/p><\/td>

2.0\u00a0 (Average)<\/span><\/p><\/td>

\u00a0<\/span><\/p><\/td>

63-67<\/span><\/p><\/td><\/tr>

\u00a0<\/span><\/p><\/td>

C-<\/span><\/p><\/td>

\u00a0<\/span><\/p><\/td>

1.7<\/span><\/p><\/td>

\u00a0<\/span><\/p><\/td>

58-62<\/span><\/p><\/td><\/tr>

\u00a0<\/span><\/p><\/td>

D+<\/span><\/p><\/td>

\u00a0<\/span><\/p><\/td>

1.3<\/span><\/p><\/td>

\u00a0<\/span><\/p><\/td>

53-57<\/span><\/p><\/td><\/tr>

\u00a0<\/span><\/p><\/td>

D<\/span><\/p><\/td>

\u00a0<\/span><\/p><\/td>

1.0\u00a0 (Pass)<\/span><\/p><\/td>

\u00a0<\/span><\/p><\/td>

50-52<\/span><\/p><\/td><\/tr>

\u00a0<\/span><\/p><\/td>

F<\/span><\/p><\/td>

\u00a0<\/span><\/p><\/td>

0\u00a0\u00a0 (Fail)<\/span><\/p><\/td>

\u00a0<\/span><\/p><\/td>

Below 50<\/span><\/p><\/td><\/tr><\/tbody><\/table>

\u00a0<\/span><\/p>

Format of the Tests and Final Examinations<\/strong><\/span><\/p>

Students are not allowed to use textbook or lecture notes during Tests\/Final Examinations. That is, close book examinations.\u00a0<\/span><\/p>

It may consist of multiple choice questions, short\/long questions. Finding solutions\/solving simple problems as well as proofs may be required.<\/span><\/p>

(It may be changed according to the arrangements to deal with covid-19 pandemic)<\/span><\/p>

\u00a0<\/p>

Discipline Requirement:<\/span><\/strong><\/span><\/p>

Usual university requirement (Cheating in any form will NOT be tolerated<\/u><\/strong>.<\/span><\/p>

General Comment:<\/span><\/strong><\/span><\/p>

All students are expected to attend all lectures, tutorials, quizzes, tests and final examination. In order to be successful in this course, students should get as much practice as possible in solving problems outside the class hours. This must be done on a timely and regular basis, as a good understanding of the material covered in any particular section of this course depends heavily on an equally good understanding of the material covered in previous sections.<\/span><\/p>

Homework Policy:<\/span><\/strong><\/span><\/p>

All homework must be an individual effort unless specifically noted. Your work must be neat, with answers clearly noted and supporting information provided. Late homework will not be accepted in general.<\/span><\/p>

Requirement<\/span>:<\/span><\/strong><\/span><\/p>

Pager, mobile phone or other communication tools will NOT be allowed to use during the time periods for lectures, tutorials, quizzes\/tests and final examination.<\/span><\/p>

Student Disabilities Support Service:<\/span><\/strong><\/span><\/p>

The University of Macau is committed to providing an equal opportunity in education to persons with disabilities. If you are a student with a physical, visual, hearing, speech, learning or psychological impairment(s) which substantially limit your learning and\/or activities of daily living, please communicate with your instructors about your impairment(s) and contact Disability Support Services in Student Affairs Office (SAO) immediately, which Student Affairs Office colleague helps coordinate and provide appropriate resources and accommodations to allow each student with a disability to have an equal opportunity in education, university life activities and services at the University of Macau. To learn more about the service, please contact Student Counselling Section in SAO at sao.disability@umac.mo, or 8822 4901 or visit the following website:\u00a0http:\/\/www.umac.mo\/sao<\/a>.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"

\u00a0 \u00a0 MATH2000 \u00a0 \u00a0Lectures: 11:30 a.m. to 12:45 p.m. (Monday & Thursday) E11-1028 \u00a0 \u00a0First 4 weeks of lecture online via ZOOM Passcode 534491 Join link https:\/\/umac.zoom.us\/j\/93687684875?pwd=MWV2K3M5WUt2aldnWlpnRzZDbW5Hdz09 \u00a0 \u00a0Tutorial: 4:00 p.m. to 4:50 p.m. (Friday) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 E11-1021 \u00a0 \u00a0 … <\/p>\n

Continue reading “MATH2000”<\/span><\/a><\/p>\n","protected":false},"author":162,"featured_media":0,"parent":16944,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"elementor_canvas","meta":{"footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-23913","page","type-page","status-publish","hentry","entry"],"_links":{"self":[{"href":"https:\/\/www.fst.um.edu.mo\/personal\/wp-json\/wp\/v2\/pages\/23913","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.fst.um.edu.mo\/personal\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.fst.um.edu.mo\/personal\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.fst.um.edu.mo\/personal\/wp-json\/wp\/v2\/users\/162"}],"replies":[{"embeddable":true,"href":"https:\/\/www.fst.um.edu.mo\/personal\/wp-json\/wp\/v2\/comments?post=23913"}],"version-history":[{"count":10,"href":"https:\/\/www.fst.um.edu.mo\/personal\/wp-json\/wp\/v2\/pages\/23913\/revisions"}],"predecessor-version":[{"id":23952,"href":"https:\/\/www.fst.um.edu.mo\/personal\/wp-json\/wp\/v2\/pages\/23913\/revisions\/23952"}],"up":[{"embeddable":true,"href":"https:\/\/www.fst.um.edu.mo\/personal\/wp-json\/wp\/v2\/pages\/16944"}],"wp:attachment":[{"href":"https:\/\/www.fst.um.edu.mo\/personal\/wp-json\/wp\/v2\/media?parent=23913"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}