Week-by-week outline
Lecture
Week Topic
1
Riemann sums
2
Definite integral:
Theory & applications
3
Further applications
4
Further applications
Indefinite integral
5
Log & exp functions
6
Introduction to
models and DEs
7
First-order DEs I
8
First-order DEs II
9
First-order DEs III
10
11
Further examples
and models
Higher-order equations
12
Systems of equations
Course Notes
Content
Upper and lower Riemann
sums Definition of definite
integral Non-positive
functions
Difference between
upper and lower
Evaluation
of integrals
Estimation of integrals and sums
Properties of the definite integral
Fundamental Theorem Part II
Areas and volumes by
slicing Integration by
substitution I Volumes
by
shells by parts
Integration
Fundamental Theorem
Part I Functions defined
by integrals
Natural
logarithm
Natural
exponential
Properties of models
Direction fields
Visualization of solution curves
Classification of differential
equations Separable equations
Integration by substitution II
Models including growth and
decay Partial fractions
Linear equations
Examples and models
Radioactive dating
Flow and mixing problems
Second-order homogeneous linear
Boundary conditions
Factorization, equal root case
Reduction to secondorder Predator-prey
systems
SHM, growing and damped
4
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 6 (except last section Trigonometric Substitutions)
Chapter7 –Integration by parts
and Reduction Formulas
Chapter 5 (first 4 pages)
Chapter 5
Chapter 8
Chapter 9
Chapter 6 last section
Chapter 7 – partial fractions
(omit Wallis Product and
Computer Algebra Systems)
Chapter 10
Chapter 11
Chapter 11
Chapter 12
Chapter 13