Optimistic Course Outline
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INTEGRAL CALCULUS:
1. Integrals (Ch. 4 & Supplementary material)
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o
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Riemann Sums
Definite and Indefinite Integrals
Darboux Definition of the Definite Integral & Reformulation
Fundamental Theorem of Calculus part I & II (FTOC)
2. Techniques of Integration (Ch. 4 & 5)
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o
o
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Substitution/Change of Variables
Integration by Parts
Partial Fraction Decompositions
Trigonometric Integrals
Trigonometric Substitution
Improper Integrals
SEQUENCES AND SERIES:
3. Sequences (Ch. 7 & Supplementary material)
o Precise limit definition & Terminology
o Properties of Convergent Sequences
o Bounded Monotonic Convergence Theorem (BMCT)
4. Series (Ch. 7)
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Definitions & Terminology
Properties (Algebra) of Convergent Series
Convergence Tests for Series
Absolute and Conditional Convergence
5. Power Series (Ch. 8)
o Power Series: Interval & Radius of Convergence
o Maclaurin Series & Taylor Series
Though we will cover most of the topics listed above, the above syllabus is not carved in stone.
We may not cover every item in the above list. Conversely, we may study an item not listed here.