MA2176 Basic Calculus and Linear Algebra

Part I

Course Duration: One semester

Credit Units: 3

Level: B2

Medium of Instruction: English

Prerequisites: Nil

Precursors: Nil

Equivalent Courses: MA1002 Higher Mathematics I(B) concurrent with MA1004 Higher Mathematics II(B)/MA2013 Basic Calculus and Linear Algebra

Exclusive Courses: MA2182 College Algebra/ MA2183 College Calculus

Part II

Course Aims

• To introduce and develop fluency in concepts and techniques from calculus and linear algebra .
• To nurture and develop skills in logical thinking and the translation of ideas using mathematical language and formalism.
• To provide students with essential mathematical training for all further study in mathematics and its applications.

Course Intended Learning Outcomes (CILOs)
Upon successful completion of this course, students should be able to:

 No. CILOs Weighting 1. describe concepts of functions and manipulate expressions involving standard functions, including rational, trigonometric, hyperbolic, exponential functions and their inverses. 2 2. manipulate and evaluate limits, derivatives, integrals and Taylor series expansions of functions in a single variable. 5 3. demonstrate fluency in vector algebra, matrix arithmetic and techniques for solving systems of linear equations. 3 4. perform basic operations and solve equations involving complex numbers. 1 5. apply mathematical methods of single variable calculus and linear algebra to a range of problems in science and engineering. 2

CILOS 1, 2, 3, 4 are the core components of the course, and CILO 5 is the synthesis of the core components used in applications.

Teaching and Learning Activities (TLAs)
(Indicative of likely activities and tasks designed to facilitate students’ achievement of the CILOs. Final details will be provided to students in their first week of attendance in this course)

Students belong to one of three broad groupings:
·        (A) for students with the greatest mathematical background and experience
·        (B) for students with a moderate mathematical background and experience
·        (C) for students with the least mathematical background and experience
Students in groupings (B) and (C) will benefit most from extra face-to-face tuition.

The following teaching and learning activities are spread evenly throughout the semester and are aligned with CILOs in approximately chronological order:

• A large class activity (lecture) engaged in learning with one instructor/lecturer
• A small interactive class (tutorial) engaged in individual learning or small group discussion with one instructor/tutor.

• Take-home assignments are extended written learning tasks which students complete
·        on their own for work which is handed in, marked and returned with comments,
·        and on their own or collaboratively for work which is not to be handed in.

• Online activities involve prepared materials available online using Blackboard, and focus primarily on computational methods and applications to problems in science and engineering.

• Remedial learning activities are provided by the Math Help Centre for students who require extra assistance.
 TLAs CILOs Hours/semester Large class activities (lectures) 1,2,3,4,5 32 (A), 39 (B,C) Small interactive classes (tutorials) 12345 0.5 (A), 2 (B,C)   3 (A), 5 (B,C)   2 (A), 3 (B,C)   1 (A), 2 (B,C)0.5 (A), 1 (B,C) Take-home assignments 1,2,3,4,5 5–8 hours after class Online activities using Blackboard 5 8 hours after class Learning activities for extra help by Math Help Centre 1,2,3,4,5 after class, depending on need

(Indicative of likely activities and tasks designed to assess how well the students achieve the CILOs. Final details will be provided to students in their first week of attendance in this course)

There are three types of assessment tasks/activities with formative and summative roles, separately or in combination:

o            Class quizzes (15-30%)

·        Regular short diagnostic quizzes are provided to monitor students’ progress and give prompt feedback.
·        These assessments are primarily formative, revealing weaknesses or gaps in knowledge or understanding.
·        Feedback to the student highlights areas or particular details where the student needs to focus more attention or seek remedial help.
·        The major focus of short quizzes is the core components CILOs 1, 2, 3, 4.

o            Assignments (15-0%)

·        One or two mini-projects are set to be handed in, marked and returned to students with comments.
·        Some assignment sheets are set, but not handed in, which students may complete individually or collaboratively, mark themselves against published (online) solutions, encouraging self-reflection and independent enquiry.
·        The successful completion of assignments will demonstrate mastery of core concepts (CILOs 1, 2, 3, 4) and provide practice in implementing mathematical methods to applications (CILO 5).
·        Assignments provide excellent practice in mathematical writing and the translation between mathematical expressions/equations and their interpretations in relevant applications.

o            Examination (70%)

·        The end of semester 3-hour examination is a thorough summative assessment.
·        The examination consists of three parts, each on a section in the Keyword Syllabus (in Part III).
·        To be given a pass grade (i.e., D or above), a student has to obtain the minimum score of each part.
·        Each part examines the extent to which students have mastered concepts and methods of the course (CILOs 1, 2, 3, 4).
·        The examination also examines students’ability to synthesize knowledge using mathematical applications in science and engineering (CILO 5).

For a student to pass the course, at least 30% of the maximum mark for the examination must be obtained.

• A−, A, A+
To achieve a grade of A, a student should
·             have complete, or close to complete, mastery of all of the core components (CILOs 1, 2, 3, 4),
·             and have demonstrated very high levels of fluency in mathematical writing and synthesis of core components, as evidenced by the successful use of mathematical methods in applications to science and engineering (CILO 5).

B−, B, B+
To achieve a grade of B, a student should
·             have good or very good mastery of all of the core components (CILOs 1, 2, 3, 4),
·             and have demonstrated good to very good levels of fluency in mathematical writing and synthesis of core components in applications to science and engineering (CILO 5).

C−, C, C+
To achieve a grade of C, a student should have good working knowledge
·             of all of the core components of the course (CILOs 1, 2, 3, 4);
·             or, alternatively, of most of the core components of the course (CILOs 1, 2, 3, 4) together with some demonstrated ability to synthesise them in applications to science and engineering (CILO 5).

D

To achieve a grade of D, a student should have some working knowledge of
·             of most of the core components of the course (CILOs 1, 2, 3, 4);
·             or, alternatively, of some of the core components of the course (CILOs 1, 2, 3, 4) together with some demonstrated ability to synthesise them in at least one application to science and engineering (CILO 5).

Keyword Syllabus

A.     Functions; Intuitive concepts of limit, continuity and differentiability; Differentiation and its applications
B.     Integration and its applications
C.     Vectors; Matrices, determinants and systems of linear equations; Complex numbers