Math 101 H
Math 101 H
This is the first of a two-semester Calculus sequence. The topics covered are somewhat similar to those in MATH 101 but this is a course where emphasis is on proofs and rigor. The course covers axiomatic development of reals, limits, continuity, differentiation and its applications, rigorous development of the Riemann Integral, techniques of integration, applications of integrals, early transcendental functions. The students will also learn to use symbolic and numerical computation software.
Schedule: Tu/Thu 10:30-11:45 Sohail Aslam Lab
Instructor's Office Hours: Tu/Thu 9-10, 12-2 (9B30 SSE Mathematics Department)
Grading Breakdown:
Assignments: 10%
Quizzes: 20%
Midterm: 30%
Final Exam: 40%
Weekly Breakdown:
Week 1: Introduction to 101H, Course goals and objectives, History of Calculus, Axiomatic construction of numbers, Field axioms.
Week 2: Ordering on a field, Well ordering principle, Supremum/Infimum, Completeness axiom, Metric structure on R.
Week3: (1 class only) Relations and Functions, Types of functions.
Week 4: Countable and Uncountable sets, Domain/Range, Composition of functions, Inverse functions, Epsilon-Delta definition of the limit.
Week 5: Computing Limits, Formal definition of continuity, Types of discontinuities.
Week 6: Continuous functions on compact domains, Bolzano's Theorem, Extreme values Theorem.
Week 7: Differential Calculus, Algebra of derivatives, Consequences of Differentiation.
Week 8: Mean value theorem and its applications, Partial derivatives and Clairaut's Theorem.
Prep Week + Midterm (Week 9)
Week 10: Taylor's polynomials and Taylor series, Error analysis.
Week 11: Introduction to integrals, Integrals using step functions, Riemann sums approximation and limiting case.
Week 12: Indefinite integrals as Antiderivatives, Techniques of integration, Fundamental theorem of Calculus.
Week 13: Differential Equations, First order separable, linear. Second order Linear ODEs. Population models, Newton's Law of Cooling, Mass spring system.
Week 14: Volumes of revolution, Disc/Washer and Shell method. Arc length of a planar curve.