# Courses tagged with "Calculus I" (77)

Electrostatics (part 1): Introduction to Charge and Coulomb's Law. Electrostatics (part 2). Proof (Advanced): Field from infinite plate (part 1). Proof (Advanced): Field from infinite plate (part 2). Electric Potential Energy. Electric Potential Energy (part 2-- involves calculus). Voltage. Capacitance. Circuits (part 1). Circuits (part 2). Circuits (part 3). Circuits (part 4). Cross product 1. Cross Product 2. Cross Product and Torque. Introduction to Magnetism. Magnetism 2. Magnetism 3. Magnetism 4. Magnetism 5. Magnetism 6: Magnetic field due to current. Magnetism 7. Magnetism 8. Magnetism 9: Electric Motors. Magnetism 10: Electric Motors. Magnetism 11: Electric Motors. Magnetism 12: Induced Current in a Wire. The dot product. Dot vs. Cross Product. Calculating dot and cross products with unit vector notation. Electrostatics (part 1): Introduction to Charge and Coulomb's Law. Electrostatics (part 2). Proof (Advanced): Field from infinite plate (part 1). Proof (Advanced): Field from infinite plate (part 2). Electric Potential Energy. Electric Potential Energy (part 2-- involves calculus). Voltage. Capacitance. Circuits (part 1). Circuits (part 2). Circuits (part 3). Circuits (part 4). Cross product 1. Cross Product 2. Cross Product and Torque. Introduction to Magnetism. Magnetism 2. Magnetism 3. Magnetism 4. Magnetism 5. Magnetism 6: Magnetic field due to current. Magnetism 7. Magnetism 8. Magnetism 9: Electric Motors. Magnetism 10: Electric Motors. Magnetism 11: Electric Motors. Magnetism 12: Induced Current in a Wire. The dot product. Dot vs. Cross Product. Calculating dot and cross products with unit vector notation.

Introduction to Waves. Amplitude, Period, Frequency and Wavelength of Periodic Waves. Introduction to the Doppler Effect. Doppler effect formula when source is moving away. When the source and the wave move at the same velocity. Mach Numbers. Specular and Diffuse Reflection. Specular and Diffuse Reflection 2. Refraction and Snell's Law. Refraction in Water. Snell's Law Example 1. Snell's Law Example 2. Total Internal Reflection. Virtual Image. Parabolic Mirrors and Real Images. Parabolic Mirrors 2. Convex Parabolic Mirrors. Convex Lenses. Convex Lens Examples. Doppler effect formula for observed frequency. Concave Lenses. Object Image and Focal Distance Relationship (Proof of Formula). Object Image Height and Distance Relationship. Introduction to Waves. Amplitude, Period, Frequency and Wavelength of Periodic Waves. Introduction to the Doppler Effect. Doppler effect formula when source is moving away. When the source and the wave move at the same velocity. Mach Numbers. Specular and Diffuse Reflection. Specular and Diffuse Reflection 2. Refraction and Snell's Law. Refraction in Water. Snell's Law Example 1. Snell's Law Example 2. Total Internal Reflection. Virtual Image. Parabolic Mirrors and Real Images. Parabolic Mirrors 2. Convex Parabolic Mirrors. Convex Lenses. Convex Lens Examples. Doppler effect formula for observed frequency. Concave Lenses. Object Image and Focal Distance Relationship (Proof of Formula). Object Image Height and Distance Relationship.

Thermodynamics (part 1). Thermodynamics (part 2). Thermodynamics (part 3). Thermodynamics (part 4). Thermodynamics (part 5). Macrostates and Microstates. Quasistatic and Reversible Processes. First Law of Thermodynamics/ Internal Energy. More on Internal Energy. Work from Expansion. PV-diagrams and Expansion Work. Proof: U=(3/2)PV or U=(3/2)nRT. Work Done by Isothermic Process. Carnot Cycle and Carnot Engine. Proof: Volume Ratios in a Carnot Cycle. Proof: S (or Entropy) is a valid state variable. Thermodynamic Entropy Definition Clarification. Reconciling Thermodynamic and State Definitions of Entropy. Entropy Intuition. Maxwell's Demon. More on Entropy. Efficiency of a Carnot Engine. Carnot Efficiency 2: Reversing the Cycle. Carnot Efficiency 3: Proving that it is the most efficient. Enthalpy. Heat of Formation. Hess's Law and Reaction Enthalpy Change. Gibbs Free Energy and Spontaneity. Gibbs Free Energy Example. More rigorous Gibbs Free Energy/ Spontaneity Relationship. A look at a seductive but wrong Gibbs/Spontaneity Proof. Stoichiometry Example Problem 1. Stoichiometry Example Problem 2. Limiting Reactant Example Problem 1. Empirical and Molecular Formulas from Stoichiometry. Example of Finding Reactant Empirical Formula. Stoichiometry of a Reaction in Solution. Another Stoichiometry Example in a Solution. Molecular and Empirical Forumlas from Percent Composition. Hess's Law Example. Thermodynamics (part 1). Thermodynamics (part 2). Thermodynamics (part 3). Thermodynamics (part 4). Thermodynamics (part 5). Macrostates and Microstates. Quasistatic and Reversible Processes. First Law of Thermodynamics/ Internal Energy. More on Internal Energy. Work from Expansion. PV-diagrams and Expansion Work. Proof: U=(3/2)PV or U=(3/2)nRT. Work Done by Isothermic Process. Carnot Cycle and Carnot Engine. Proof: Volume Ratios in a Carnot Cycle. Proof: S (or Entropy) is a valid state variable. Thermodynamic Entropy Definition Clarification. Reconciling Thermodynamic and State Definitions of Entropy. Entropy Intuition. Maxwell's Demon. More on Entropy. Efficiency of a Carnot Engine. Carnot Efficiency 2: Reversing the Cycle. Carnot Efficiency 3: Proving that it is the most efficient. Enthalpy. Heat of Formation. Hess's Law and Reaction Enthalpy Change. Gibbs Free Energy and Spontaneity. Gibbs Free Energy Example. More rigorous Gibbs Free Energy/ Spontaneity Relationship. A look at a seductive but wrong Gibbs/Spontaneity Proof. Stoichiometry Example Problem 1. Stoichiometry Example Problem 2. Limiting Reactant Example Problem 1. Empirical and Molecular Formulas from Stoichiometry. Example of Finding Reactant Empirical Formula. Stoichiometry of a Reaction in Solution. Another Stoichiometry Example in a Solution. Molecular and Empirical Forumlas from Percent Composition. Hess's Law Example.

This is an introduction to quantum computation, a cutting edge field that tries to exploit the exponential power of computers based on quantum mechanics. The course does not assume any prior background in quantum mechanics, and can be viewed as a very simple and conceptual introduction to that field.

Nanotechnology is an emerging area that engages almost every technical discipline – from chemistry to computer science – in the study and application of extremely tiny materials. This short course allows any technically savvy person to go one layer beyond the surface of this broad topic to see the real substance behind the very small.

Fluids (part 1). Fluids (part 2). Fluids (part 3). Fluids (part 4). Fluids (part 5). Fluids (part 6). Fluids (part 7). Fluids (part 8). Fluids (part 9). Fluids (part 10). Fluids (part 11). Fluids (part 12). Fluids (part 1). Fluids (part 2). Fluids (part 3). Fluids (part 4). Fluids (part 5). Fluids (part 6). Fluids (part 7). Fluids (part 8). Fluids (part 9). Fluids (part 10). Fluids (part 11). Fluids (part 12).

Relationship between angular velocity and speed. Why Distance is Area under Velocity-Time Line. Introduction to Vectors and Scalars. Calculating Average Velocity or Speed. Solving for Time. Displacement from Time and Velocity Example. Acceleration. Balanced and Unbalanced Forces. Unbalanced Forces and Motion. Newton's First Law of Motion. Newton's First Law of Motion Concepts. Newton's First Law of Motion. Newton's Second Law of Motion. Newton's Third Law of Motion. Airbus A380 Take-off Time. Airbus A380 Take-off Distance. Average Velocity for Constant Acceleration. Acceleration of Aircraft Carrier Takeoff. Race Cars with Constant Speed Around Curve. Introduction to Gravity. Mass and Weight Clarification. Gravity for Astronauts in Orbit. Would a Brick or Feather Fall Faster. Deriving Displacement as a Function of Time, Acceleration and Initial Velocity. Plotting Projectile Displacement, Acceleration, and Velocity. Projectile Height Given Time. Deriving Max Projectile Displacement Given Time. Impact Velocity From Given Height. Visualizing Vectors in 2 Dimensions. Projectile at an Angle. Different Way to Determine Time in Air. Launching and Landing on Different Elevations. Total Displacement for Projectile. Total Final Velocity for Projectile. Correction to Total Final Velocity for Projectile. Projectile on an Incline. Unit Vectors and Engineering Notation. Clearing the Green Monster at Fenway. Green Monster at Fenway Part 2. Optimal angle for a projectile part 1. Optimal angle for a projectile part 2 - Hangtime. Optimal angle for a projectile part 3 - Horizontal distance as a function of angle (and speed). Optimal angle for a projectile part 4 Finding the optimal angle and distance with a bit of calculus. Slow Sock on Lubricon VI. Normal Forces on Lubricon VI. Normal Force and Contact Force. Normal Force in an Elevator. Inclined Plane Force Components. Ice Accelerating Down an Incline. Force of Friction Keeping the Block Stationary. Correction to Force of Friction Keeping the Block Stationary. Force of Friction Keeping Velocity Constant. Intuition on Static and Kinetic Friction Comparisons. Static and Kinetic Friction Example. Introduction to Tension. Introduction to Tension (Part 2). Tension in an accelerating system and pie in the face. Introduction to Momentum. Momentum: Ice skater throws a ball. 2-dimensional momentum problem. 2-dimensional momentum problem (part 2). Introduction to work and energy. Work and Energy (part 2). Conservation of Energy. Work/Energy problem with Friction. Introduction to mechanical advantage. Mechanical Advantage (part 2). Mechanical Advantage (part 3). Center of Mass. Introduction to Torque. Moments. Moments (part 2). Unit Vector Notation. Unit Vector Notation (part 2). Projectile Motion with Ordered Set Notation. Projectile motion (part 1). Projectile motion (part 2). Projectile motion (part 3). Projectile motion (part 4). Projectile motion (part 5). Centripetal Force and Acceleration Intuition. Visual Understanding of Centripetal Acceleration Formula. Calculus proof of centripetal acceleration formula. Loop De Loop Question. Loop De Loop Answer part 1. Loop De Loop Answer part 2. Acceleration Due to Gravity at the Space Station. Space Station Speed in Orbit. Conservation of angular momentum. Introduction to Newton's Law of Gravitation. Gravitation (part 2). Viewing g as the value of Earth's Gravitational Field Near the Surface. Intro to springs and Hooke's Law. Potential energy stored in a spring. Spring potential energy example (mistake in math). Introduction to Harmonic Motion. Harmonic Motion Part 2 (calculus). Harmonic Motion Part 3 (no calculus).

Quantum computation is a remarkable subject building on the great computational discovery that computers based on quantum mechanics are exponentially powerful. This course aims to make this cutting-edge material broadly accessible to undergraduate students, including computer science majors who do not have any prior exposure to quantum mechanics. The course starts with a simple introduction to the fundamental principles of quantum mechanics using the concepts of qubits (or quantum bits) and quantum gates. This treatment emphasizes the paradoxical nature of the subject, including entanglement, non-local correlations, the no-cloning theorem and quantum teleportation. The course covers the fundamentals of quantum algorithms, including the quantum fourier transform, period finding, Shor's quantum algorithm for factoring integers, as well as the prospects for quantum algorithms for NP-complete problems. It also discusses the basic ideas behind the experimental realization of quantum computers, including the prospects for adiabatic quantum optimization and the D-Wave controversy.

Before your course starts, try the new edX Demo where you can explore the fun, interactive learning environment and virtual labs. Learn more.

**Do I need a textbook for this class?**

No. Notes will be posted each week. If you wish to consult other references, a list of related textbooks and online resources will be provided.

**What is the estimated effort for course?**

About 5-12 hrs/week.

**Why is the work load range so wide?**

How long you spend on the course depends upon your background and on the depth to which you wish to understand the material. The topics in this course are quite open ended, and will be presented so you can understand them at a high level or can try to follow it at a sophisticated level with the help of the posted notes.

**How much does it cost to take the course?**

Nothing! The course is free.

**Will the text of the lectures be available?**

Yes. All of our lectures will have transcripts synced to the videos.

**Do I need to watch the lectures live?**

No. You can watch the lectures at your leisure.

You understand velocity and acceleration well in one-dimension. Now we can explore scenarios that are even more fun. With a little bit of trigonometry (you might want to review your basic trig, especially what sin and cos are), we can think about whether a baseball can clear the "green monster" at Fenway Park. Visualizing Vectors in 2 Dimensions. Projectile at an Angle. Different Way to Determine Time in Air. Launching and Landing on Different Elevations. Total Displacement for Projectile. Total Final Velocity for Projectile. Correction to Total Final Velocity for Projectile. Projectile on an Incline. Unit Vectors and Engineering Notation. Clearing the Green Monster at Fenway. Green Monster at Fenway Part 2. Unit Vector Notation. Unit Vector Notation (part 2). Projectile Motion with Ordered Set Notation. Optimal angle for a projectile part 1. Optimal angle for a projectile part 2 - Hangtime. Optimal angle for a projectile part 3 - Horizontal distance as a function of angle (and speed). Optimal angle for a projectile part 4 Finding the optimal angle and distance with a bit of calculus. Race Cars with Constant Speed Around Curve. Centripetal Force and Acceleration Intuition. Visual Understanding of Centripetal Acceleration Formula. Calculus proof of centripetal acceleration formula. Loop De Loop Question. Loop De Loop Answer part 1. Loop De Loop Answer part 2. Visualizing Vectors in 2 Dimensions. Projectile at an Angle. Different Way to Determine Time in Air. Launching and Landing on Different Elevations. Total Displacement for Projectile. Total Final Velocity for Projectile. Correction to Total Final Velocity for Projectile. Projectile on an Incline. Unit Vectors and Engineering Notation. Clearing the Green Monster at Fenway. Green Monster at Fenway Part 2. Unit Vector Notation. Unit Vector Notation (part 2). Projectile Motion with Ordered Set Notation. Optimal angle for a projectile part 1. Optimal angle for a projectile part 2 - Hangtime. Optimal angle for a projectile part 3 - Horizontal distance as a function of angle (and speed). Optimal angle for a projectile part 4 Finding the optimal angle and distance with a bit of calculus. Race Cars with Constant Speed Around Curve. Centripetal Force and Acceleration Intuition. Visual Understanding of Centripetal Acceleration Formula. Calculus proof of centripetal acceleration formula. Loop De Loop Question. Loop De Loop Answer part 1. Loop De Loop Answer part 2.

Linear momentum. Conservation of momentum. Elastic collisions. Introduction to Momentum. Momentum: Ice skater throws a ball. 2-dimensional momentum problem. 2-dimensional momentum problem (part 2). Introduction to Momentum. Momentum: Ice skater throws a ball. 2-dimensional momentum problem. 2-dimensional momentum problem (part 2).

Thinking about making things rotate. Center of mass, torque, moments and angular velocity. Center of Mass. Introduction to Torque. Moments. Moments (part 2). Relationship between angular velocity and speed. Conservation of angular momentum. Center of Mass. Introduction to Torque. Moments. Moments (part 2). Relationship between angular velocity and speed. Conservation of angular momentum.

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