**Syllabus for M113 –
Applied Calculus and Finite Mathematics 1 - Fall 2008**

Lecture Notes on Calculus of Structures (CS) by Jay Kappraff

Additional Notes (K) by Jay Kappraff

Additional Notes and problems (AN)

**Week 1**

Math laboratory

Go over lab problems,

Ungraded algebra quiz

Lines – K

**Week 2**

Lines - K

Functions – K,

Areas - K

Rate of change – K

**Week 3**

Functions - K

Graphing simple curves

Signed areas - K

Signed areas and problems of motion – Distance and accumulated rate of
change - K

Accumulated rate of change and the integral - K

**Week 4**

CS Lesson 1 - equilibrium of forces,
moments, determinate and indeterminate systems.

CS Lesson 2 – Determine shear force and bending moment for a
concentrated load using a) Method 1 -architectural structures; b) Method 2 -
the method of areas; and c) Method 3 - the method of slopes.

Go over solution to problems of CS Lesson 2

**Week 5**

CS Lesson 2 - Additional beam problems, Cantilever beam

CS Lesson 3 –continuous loads with constant density using
Method 1 and 2,
Solution to problem with continuous loads

Center of gravity

CS Lesson 4 - Introduction to slopes of curves.

**Week 6**

Exam 1

Limits - K

CS Lesson 4 - The derivative and the slope of the tangent
line to a curve

Derivatives of x^{2}, 1/x using
the “derivative machine.”

**Week 7**

Derivatives of x^{3} and cos
x by the derivative machine

CS Lesson 5 - Multiplication rule, sum and difference rule
for derivatives, power law, anti-derivatives, polynomials and their derivatives

Practice problems with derivatives and anti-derivatives - AN

**Week 8**

Practice with differentiation - AN

Practive with antiderivatives
- AN

CS Lesson 6 - Use of antiderivatives
to find areas,

CS Lesson 7 – Proof that the shear force is the derivative
of the bending moment.

CS Lesson 8 - Solution of the continuous load problem by
integrals.

**Week 9**

CS Lesson 7 - Fundamental law of calculus
.

Absolute maxima and minima on a closed interval – AN

Curve sketching using the first derivative - AN

CS Lesson 8 - Application of integrals to solving beam
problems.

**Week 10**

Exam 2

Curve sketching, second derivative and curvature - AN

Optimization – AN

CS Lesson 8- Solutions to beam problems using integrals

Logs and exponentials and their derivatives – K, AN

**Week 11**

Exam 2

More max-min problems – K, AN

CS
Lesson 9 - Maximum load on a beam.

CS Lesson 11 – Product and quotient, rules for derivatives

**Week 12**

Practice problems for product and quotient - AN

CS Lesson 10 - Deflection of a beam.

Moments of inertia

**Week 13**

Chain rule for derivatives, Related rates – AN

CS Lesson 12 - Center of gravity and centroids,
conjugate beam method for finding deflection

**Week 14**

Computation of center of gravity by integrals

Practice with derivatives, more max – min problems.

Indeterminate structures - K

Film on structures

**Week 15 **

Review

**Final Exam**

**Course Mechanics:**

**Telephone: x3490**

**e-mail****: kappraff@adm.njit.edu**

**Room: 208a Cullimore Hall**

**Website:
www-ec.njit.edu/~kappraff**

**Attendance is
required. Three unexcused absences will
be permitted. If you cannot attend a class
you must notify me by e-mail before the class giving a reason for you absence.**

**There will be two
in-class exams and a final. You will
also be expected to keep a scrapbook of interesting structures indicating
wherever possible the elements of structures discussed in the class. Homework will be regularly assigned and
graded. The homework will be posted on
my website. There will be several
quizzes given in class. The grade will
be calculated as follows:**

**Exam 1 – 22 %**

**Exam 2 – 22%**

**Final - 36%**

**Scrapbook, Homework,
and quizzes - 20%**

** **