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

Week 1

Math laboratory

Go over lab problems,

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 x2, 1/x using the “derivative machine.”

Week 7

Derivatives of  x3 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

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%