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MATA32H3 (200)
Lecture 1

MATA32H3 Lecture Notes - Lecture 1: Logarithmic Differentiation, Differentiation Rules, Antiderivative


Department
Mathematics
Course Code
MATA32H3
Professor
Xiamei Jiang
Lecture
1

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Course Syllabus and Lecture Schedule
2015 Winter
(This schedule is a guideline and it is possible that there may be small changes to the ordering or
duration of course topics as the course proceeds. All chapter and section references are in the
textbook, "Introductory Mathematical Analysis" 13th edition, by Haeussler, Paul and Wood)
Week 1: Introduction to MATA32. Lecture review of functions, operations, exponential and
logarithmic functions (Sections 2.1 - 2.5 and 4.1 - 4.4). Please review Chapters 0, 1 and 3 as
necessary. Omit sections 2.6 – 2.8.
Week 2: Introduction to Mathematics of Finance: compound interest, present and future
value, effective rate, equations of value (Sections 5.1 and 5.2).
Week 3: Mathematics of finance continued: continuously compounding interest, effective
rate, annuities, amortization (Sections 5.3 - 5.5. Section 1.5 on summation notation is relevant
too). Omit section 5.6.
.
Week 4: Limits and continuity: limits at a point, infinite limits and limits at infinity,
continuity (Sections 10.1 - 10.3). Omit section 10.4.
Week 5: Differentiation: the derivative and tangent line concept, differentiation rules,
interpretation of the derivative in the context of economics, the marginal concept (Sections
11.1 - 11.4).
Week 6: Additional topics in differentiation: Chain Rule, Implicit Differentiation, derivatives of
logarithmic/exponential functions, higher derivatives (Sections 11.5, 12.1, 12.2, 12.5 and 12.7).
Omit section 12.6.
Week 7: Review. Elasticity of demand, logarithmic differentiation. (Sections 12.3, 12.4).
Week 8: Applications of derivatives and curve sketching: monotonicity, extrema, extrema on a
closed interval, curve sketching, concavity. (Sections 13.1 -13.3)
applications in economics, derivative tests, asymptotes and curve sketching continued, (Sections
13.2 – 13.5).
Week 9: Derivative tests, asymptotes and curve sketching continued, Extrema problems in
economics (Sections 13.4 – 13.6)
Week 10: Integration: the indefinite integral, integration with initial conditions, applications
in economics, elementary techniques of integration substitution, manipulations, (Sections 14.2 –
14.5). Omit section 14.1.
Week 11: Integration continued: integration by parts, the definite integral, fundamental theorem
of calculus, area, applications in economics (Sections 15.1, 14.6 - 14.7) Omit section 14.8.
Week 12: Integration continued: area between curves, vertical and horizontal elements,
consumers' and producers' surplus (Sections 14.9 - 14.10).
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