Curriculum Syllabus & Outline
Markdown Syllabus# Math 154 Outline
1. Functions & Models
2. Limits & Derivatives
3. Differentiation Rules
4. Applications (rates, optimization)
5. Integrals & FTC
6. Applications (work, hydrostatic pressure)
7. Differential Equations (intro)
Educational Context & Standards
Math 154 is calculus I for engineers, emphasizing applications in physics and engineering: work, pressure, center of mass.
Cross-Curriculum Equivalents
Canada/ON: University of Toronto / Waterloo MAT135 / MATH137
CA-ON-U-CALC1
Canada/AB: University of Alberta MATH 114 / 117
CA-AB-U-CALC1
US/National: AP Calculus AB / BC & Collegiate Calc I
US-AP-CALC-BC
US/NY: SUNY / Columbia Calculus I (MATH UN1101)
US-NY-COL-CALC1
US/TX: UT Austin M 408C / Texas A&M MATH 151
US-TX-UTA-M408
Structured Lesson Modules (6 Lessons)
1
Functions & Models
Linear, polynomial, rational, exponential models.
2
Limits & Derivatives
Definition and rules.
3
Applications
Related rates, optimization.
4
Integrals
Antiderivatives, FTC, substitution.
5
Engineering Applications
Work, pressure, center of mass.
6
Intro DE
Growth/decay models.
Assessments & Check-for-Understanding
Q1
Work = ∫ ?
Answer
F(x) dx
Q2
Hydrostatic pressure at depth h?
Answer
ρ g h
Q3
Center of mass x̄ = ?
Answer
∫x ρ dx / ∫ρ dx
Q4
Derivative of a^x?
Answer
a^x ln a
Q5
∫ sec² x dx = ?
Answer
tan x + C
Q6
Newton's law cooling?
Answer
dT/dt = -k(T-T_env)