Calculus-based physics
Undergraduate · Physics
Syllabus focus
Standard syllabus · STEM / applied
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$60.00 · 60 min · Undergraduate · Online ($60/hr)
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Topics typically covered
Standard syllabus
Calculus-enhanced mechanics
- Instantaneous velocity and acceleration from derivatives
- Integrals for work, impulse, and center of mass
- Differential equations for damped oscillations (intro)
- Variable force problems using integration
- Energy methods with potential energy functions
Rotational and oscillatory systems
- Angular kinematics with calculus
- Torque and angular momentum as vector quantities
- Small-angle approximations for pendulums
- Coupled oscillators and normal modes (overview)
- Rolling without slipping constraints
Fields and circuits
- Electric and magnetic fields with vector notation
- Gauss's law integrals for symmetric charge distributions
- RC circuit charging as exponential decay
- Maxwell's equations in integral form
- Wave equation for electromagnetic radiation
STEM / applied
Computational problem solving
- Euler method for projectile motion with drag
- Symbolic differentiation checks on homework
- Plotting fields and equipotentials
- Fitting experimental data with linearized models
- Using CAS tools for routine integrals
Engineering design problems
- Beam deflection and Hooke's law extensions
- Heat exchanger and conduction models
- Filter circuits and frequency response
- Rocket staging and variable mass (qualitative)
- Optimization of launch angles and energies
Instrumentation labs
- Calculus-based error analysis with partial derivatives
- Differentiating position signals to velocity
- Integrating current to find charge stored
- Comparing analytic and numerical solutions
- Technical communication with equations and units
Notes
Topics reflect common coverage in US university physics syllabi (OpenStax University Physics, Young & Freedman, and similar sequences). Exact order, depth, and applied emphasis vary by institution and instructor.